Yes, Brahman is Androgynous, but he/she does not have desire of opposite sex, because He is complete in himself and is spiritual consciousness,hence he is called Purna(complete) Purusha Paramatma(Supersoul).
Ardhnarishshvara(Fusion of Shiva/Brahman and Shakti/Maya/Vishnu is the true form of Brahman )
As per Bhagwat Geeta
ye tv aksaram anirdesyam avyaktam paryupasate sarvatra-gam acintyam ca
kuta-stham acalam dhruvam sanniyamyendriya-gramam sarvatra
sama-buddhayah te prapnuvanti mam eva sarva-bhuta-hite ratah
But those who fully worship the unmanifested, that which lies beyond
the perception of the senses, the all-pervading, inconceivable, fixed,
and immovable-the impersonal conception of the Absolute Truth-by
controlling the various senses and being equally disposed to everyone,
such persons, engaged in the welfare of all, at last achieve Me i.e.
Nirakaar Brahman Purusha.
Explained in Upanishads
In the beginning this was Self alone, in the shape of a person
(Puruṣa). He looking around saw nothing but his Self (Atman). He first
said, "This is I", therefore he became I by name.
—Brihadaranyaka Upanishad 1.4.1
Higher than the senses, stand the objects of senses. Higher than
objects of senses, stands mind. Higher than mind, stands intellect.
Higher than intellect, stands the great self/soul. Higher than the great
self, stands Avyaktam. Higher than Avyaktam, stands Purusha. Higher
than this, there is nothing. He is the final goal and the highest
point. In all beings, dwells this Purusha, as Atman (soul), invisible,
concealed. He is only seen by the keenest thought, by the sublest of
those thinkers who see into the subtle.
—Katha Upanishad 3.10-13
Even, science has proofed today that man has XY sex chromosomes while a woman has XX chromosomes and man's gametes actually control the gender of child. God created man in his own image(androgynes XY chromosomes) and woman in the image of his left half Shakti(XX chromosomes).
Ramakrishna regarded the Supreme Being to be both Personal and Impersonal, active and inactive:
When I think of the Supreme Being as inactive - neither creating nor
preserving nor destroying - I call Him Brahman or Purusha, the
Impersonal God. When I think of Him as active - creating, preserving
and destroying - I call Him Sakti or Maya or Prakriti, the Personal
God. But the distinction between them does not mean a difference. The
Personal and Impersonal are the same thing, like milk and its
whiteness, the diamond and its lustre, the snake and its wriggling
motion. It is impossible to conceive of the one without the other. The
Divine Mother and Brahman are one
Kabir Das used to say: 'God with form is my Mother, the formless
God my Father. Whom should I blame? Whom should I adore? The two
sides of the scales are even.' During the day-time Haladhari used to
meditate on God with form, and at night on the formless God. Whichever
attitude you adopt, you will certainly realize God if you have firm
faith. You may believe in God with form or in God without form, but
your faith must be sincere and whole-hearted."
Is there any sex-distinction in the Atman (Self)? Out with the
differentiation between man and woman—all is Atman! Give up the
identification with the body, and stand up!
Worship of society and popular opinion is idolatry. The soul has no
sex, no country, no place, no time.
PRAY ALL THE TIME, READ ALL THE SCRIPTURES IN THE WORLD, AND WORSHIP
ALL THE GODS THERE ARE ... UNLESS YOU REALIZE THE SELF(ATMAN), THERE
IS NO FREEDOM
Brahman is both Purusha and Prakriti and is pure spiritual cosmic consciousness, hence he himself is Brahmanchari/celibate.
"shudhama poapvidham" "He is bodyless and pure." [Yajurveda 40:8] i.e. Nirakaar Brahman Purusha
Ramakrishna taught that the primal bondage in human life is Kama-Kanchana (lust and gold). When speaking to men, Ramakrishna warned them against kamini-kanchana, or "women and gold"
Only a perfect Bramhamchari alone can understand Purusha/Brahman and attain Kaivalya.