TL;DR No, this is inappropriate. However, according to the Vedas, you certainly can worship a deity/devatha of your choice. It must be noted that madhurya bhava is not something one can imitate. It is something that occurs naturally towards one's ishta devata when one is in advanced stages of devotion.
Below, I am going to present what the Vaishnava perspective (that I am familiar with) is describing the position of different gods in relation to the Supreme Atma. The Supreme Atma is identified to be Narayana, for He alone is the Paramatma of all living entities including the gods and goddesses and He alone has a śarīra-śarīri relationship with all living entities. For instance, the Subala Upanishad, as well as the Bruhadaranyaka Upanishad declare
"He for whom the ātmā is the body" (Madhyandina recension of Brhadaranyaka Upanishad 3.7.22).
In other words, all jivāthmas (including various gods and goddesses) form the body of Paramāthma.
This idea is supported in the Ramayana, wherein we find Lord Brahma declaring to Lord Rama that the entire cosmos consisting of all sentient and non-sentient beings is His body:
jagat sarvam śarīram the (Ramayana 6.117.26)
and he mentions that he himself, his consort Saraswati, and the other gods created by him form His body:
aham te hṛdayaṁ rāma
jihvā devī saraswatī
deva romāṇi gātreṣu
brahmaṇā nirmitāḥ prabho (6.117.24)
And in the Vishnu Purana:
tat sarvam vai hares tanuḥ
also supporting the same idea that everything is the body of Lord Hari
Now, further references from Bhagavad Gita
pitāham asya jagato mātā dhātā pitāmahaḥ vedyaṁ (9.17)
"Know Me to be the Father, Mother, the Supporter and the Grandfather of the entire cosmos"
gatir bhartā prabhuḥ sākṣī nivāsaḥ śaraṇaṁ suhṛt (9.18)
"I am the Goal, the Maintainer, the Master, the Witness, the Resting Place, the Refuge and the Best Friend"
Acharyas and Azhwars such as Kulasekhara have also talked about the nine types of relationship between the jivatma and the Paramatma. For instance, see this.
So, it is appropriate to develop such feelings only toward Him. For, it is said by Narada to Yudhistira,
nirvaireṇa bhayena vā
snehāt kāmena vā yuñjyāt
kathañcin nekṣate pṛthak" (7.1.26)
Manifesting such feelings toward other gods is artificial and improper for the following reasons:
- The gods are eternally parts and parcels of Narayana and do not have an independent existence. For instance, we find the following statements in the Upanishads and Puranas:
"mamaivāṁśo jīva-loke jīva-bhūtaḥ sanātanaḥ" - Bhagavad Gita 15.7
"All jivas (including gods) are His amśas."
yathā taror mūla-niṣecanena
prāṇopahārāc ca yathendriyāṇāṁ
tathaiva sarvārhaṇam acyutejyā (Bhagavatam 4.31.14)
"Just as by watering the root of a tree, one satisfies its branches, twigs and leaves, and by supplying food to the stomach one satisfies all the senses of the body, similarly, by engaging in the service of the Supreme Lord one automatically satisfies all the gods and all other living entities."
The Antaryami Brahmana (3.7.2 to 3.7.23 or so) of the Brhadarnayaka Upanishad gives many statements of the type -
“yaṁ pṛthivyām tiṣtan prithivyāntaro yaṁ pṛthivī na vedā"
"yasya pṛthivī śarīram yā pṛthivīm antaro yamayati sa ta ātmā antaryāmi amrtā”
which all essentially convey the idea that He, Narayana, exists as the inner controller of all these elements such as the sun, the earth, the eye, the fire, the water, the organs, the intellect etc.
And, all worships of gods go to Him alone (but that is indirect), as stated in:
"ye 'py anya-devatā-bhaktā
te 'pi mām eva kaunteya
yajanty avidhi-pūrvakam" - 9.23 Bhagavad Gita
- Because the gods do not have an independent existence, they cannot sanction anything independently.
Whatever is requested of them by a candidate worshiping them, is only sanctioned ultimately by Narayana but through their agency.
"mayaiva vihitān hi tān" - Bhagavad Gita 7.22
- By such worship of gods for desires, will eventually take one to the worlds of the gods.
"yānti deva-vratā devān" (Those who worship the gods go to the gods) - BG 9.25
but all such planets will get destroyed all the way until Brahma's at the time of total dissolution (maha-pralaya).
"ā-brahma-bhuvanāl lokāḥ punar āvartino 'rjuna.." (Bhagavad Gita 8.16)
Neither the gods themselves nor their abodes are therefore permanent and an intelligent person is not after temporary things.
"tasyaiva hetoḥ prayateta kovido
na labhyate yad bhramatām upary adhaḥ" (Bhagavatam 1.5.18)
- gods are different appointed agents of God for universal administration and each of them is in charge of a particular department. For a good wife, or good husband, or good health, or good wealth, or good knowledge, for success, etc. one worships a particular god. The Supreme Being, Sriman Narayana is like the CEO. Worship of gods is usually for some material benefit and is usually for selfish fulfilment of selfish desires.
"kāmais tais tair hṛta-jñānāḥ prapadyante 'nya-devatāḥ" -
those whose intelligence is stolen by material desires of various types surrender to other gods (instead of Me, says Krishna) - (Bhagavad Gita - 7.20)
But the fruits given by them are also temporary:
"antavat tu phalaṁ teṣāṁ
tad bhavaty alpa-medhasām
devān deva-yajo yānti
mad-bhaktā yānti mām api" (Bhagavad Gita 7.23)
"Men of small intelligence worship the gods, and their fruits are limited and temporary. Those who worship the gods go to the worlds of the gods, but My devotees reach My supreme planet."
One might then ask why worship of various gods and goddesses is mentioned in the Vedas. Because people of this world don't always desire the highest goal of liberation. They are more interested in temporary benefits of one kind or another. This squarely summarizes "conditioned existence". Because the Vedas are broad-minded and are said to have the compassion of a million mothers (Gita Bhashyam, Ramanujacharya, 2.46 purport), they sanction such approaches as mentioned in this verse of Bhagavad Gita:
"yāvān artha udapāne
tāvān sarveṣu vedeṣu
brāhmaṇasya vijānataḥ (2.46)"
"For a person who knows the self, all the Vedas are only of so much use as a flooded water reservoir is for a thirsty person."
(Purport by Ramanujacharya for this verse): All that is taught in the Vedas is not suitable to be practiced by everyone. A reservoir, which is completely overflowing with water is constructed for all kinds of purposes like irrigation etc. The thirsty person will only use enough to quench his thirst and not the entire content. Likewise, an enlightened aspirant seeking liberation will only take from the Vedas that which contributes directly to Liberation, and nothing else.
So one need not aspire for other benefits or forms of worship just because they exist.
The proper feeling toward other gods is one of reverence. One must respect them and offer due regards and obeisances to them, by all means. Daksha failed to offer proper regards to Lord Shiva and offended both Lord Shiva and Sati Devi, and got himself beheaded because of his attitude.
Even toward Narayana, feelings of madhurya bhava are artificial to manifest immediately unless one has advanced by leaps and bounds in devotional service in previous lives. Souls such as Mirabai, Godadevi, etc are exceptions. One should not imitate but begin with reverential devotional service which will naturally, in course of time, if properly applied, mature according to one's application in a particular way. This is what authoritative acharyas in all sampradayas have taught.
Putting it all together,
(Stage 1) one can go to the gods to fulfill one's material desires. That is okay, and allowed according to the Vedas. But manifesting madhurya bhava toward Radha or Lakshmi or Parvati is not appropriate. Ravana had so much lust that he was not satisfied after getting any number of good looking women. He went all the way to the Goddess of Fortune. He got himself destroyed. So, it might even be better to be an atheist and not have any faith in any form of God than lust after goddesses artificially. That is extremely injurious.
(Stage 2) If one recognizes Narayana as the Supreme Overlord of everything and directly go to Him for material desires, that is better.
(Stage 3) If one goes to Him only for liberation, giving up material desires altogether that is even better.
(Stage 4) If one goes to Him desiring Him alone and relationship with Him, that is the best.
If one is still attached to a particular god, but willing to move forward toward liberation, one can pray to that god to increase their devotion to Narayana. They would feel quite fulfilled by your desire and bless you with all their hearts to move forward. Vaishnava acharyas, in particular, have disallowed their followers from the adoration of other gods and goddesses because they did not want their followers to lose track of the goal of life, namely, liberation. But they never recommended disrespect of anyone. For instance, Madhvacharya says:
Pūjyā devās tataḥ sadā: "the gods are always to be offered respect"
People in the Sampradaya of Shankaracharya even worship all gods but with the understanding that they are, indeed, worshiping the Inner Soul within of all these gods.
Now regarding your specific question of Radha, Lakshmi or Parvati, Lakshmi or Radha are compassion potencies of the Lord and are often portrayed as mediatrices between the Lord and the jiva i.e., one takes shelter of Lakshmi/Radha to attain Narayana/Krishna. The way one takes shelter is, by considering them as a mother. If you've wronged against your father, you first try to go to your mother and then through your mother, reach the father. For example, Ramanujacharya prays in the Saranagati Gadya (verse 1):
"akhila jagan mātaram asman mātaram.. saraṇam aham prapadye." - O mother of the entire universe, my own mother, I surrender to thee (to reach the Supreme Father).
An acharya is, however, to be worshiped even greater than God because he is the one who gives access to God. He reconnects everyone to God. Therefore, we still worship Sankaracharya, Ramanujacharya, Madhvacharya, etc. But such sad-acharyas are also extremely rare.
I have presented what I have learned from acharyas. In my attempt to present this picture, I hope I have not offended anyone's feelings. My due apologies.