We can't say for sure if reading this particular stotram gives the reader occult powers (i think you meant siddhis by that).
What one achieves upon reciting a stotram/kavacham is usually found in the phalasruti given at its end . In this case the author simply does not mention anything at all.
The last stanza of the stotram says only this:
अयि मयि दीन दयालुतया कृपयैव त्वया भवितव्यमुमे अयि जगतो जननी कृपयासि
यथासि तथानुमितासिरते । यदुचितमत्र भवत्युररीकुरुतादुरुतापमपाकुरुते जय
जय हे महिषासुरमर्दिनि रम्यकपर्दिनि शैलसुते ॥ २१ ॥
Ayi Mayi Diina Dayaalu-Tayaa Krpaya-Iva Tvayaa Bhavitavyam-Ume Ayi
Jagato Jananii Krpayaasi Yathaasi Tathanu-mita-Asira-Te |
Yad-Ucitam-Atra Bhavatyurarii-Kurutaa-Duru-Taapam-Apaakurute Jaya Jaya
He Mahissaasura-Mardini Ramya-Kapardini Shaila-Sute || 21 ||
21.1: (Salutations to the Divine Mother) You Must Bestow Your Grace on Me, O Mother Uma, Who is Compassionate to the Miserable.
21.2: O Mother of the Universe; Just as Your Grace is Showered (on the Devotees), In the Same Manner are Your Arrows Scattered (on the
21.3 Please do Whatever is Appropriate at this time, O Worshipful Mother, to Remove My Sorrows and Afflictions which has become
Difficult for me to bear.
21.4: Victory to You, the Destroyer of the Demon Mahishasura, Who has Beautiful Locks of Hair and Who is the Daughter of the Mountain.
To understand what i am saying you can see Sri Adi Shankara's Lalita Pancha Ratnam Stotram. Here, the phalasruti says:
Ya sloka panchakam idham, Lalithambikya, Soubhagyuam, sulalitham
patathi prabhathe, Thasmai dadathi lalitha jadithi prasanna, Vidhyaam
sriyam vimala soukha manantha keerthim.
He who reads these five stanzas, In the morning , extolling the mother
Lalitha,. Who is easy to please
Would get luck, knowledge riches, endless fame By the grace of Goddess Lalitha.
So, we know for sure what are achieved by reading this particular stotram and its clearly mentioned by the author himself.
Here is another stotram dedicated to Sri Lalita Mahatripurasundari called Sri Lalita Pancha Vimsati Nama Stotram (Pancha Vimasati is 25). This stotram is from the Brahmanda Purana. Its being told by Sri Hayagriva to Agastya Muni. Here, author clearly mentions that upon reading this stotram siddhis or super natural powers are obtained.
स्तुवन्ति ये महाभागां ललितां परमेश्वरीम् | ते प्राप्नुवन्ति
सौभाग्यमष्टौ सिद्धीर्महद्यश: |6|
stuvanti ye mahAbhAgAM lalitAM parameshvarIm |
te prApnuvanti saubhAgyam-aShTau siddhIr-mahadyashaH ||
One who recites these twenty-five names shall attain eight great
spiritual-accomplishments, prosperity and fame.
So, IMO, the answer to your question will be " we can't say for sure since the author himself has not mentioned any thing of that sort."