Yes they can. Enlightenment depends on development of the mind. The idea of a man or a woman is a concept and has no basis in reality. You can not find a man or a woman in a moment of seeing, hearing, smelling, tasting, touching, or thinking. So, the question itself is based on wrong understanding of reality.
You can see the Soma Sutta where a nun responds to this very question:
What
difference
does being a woman make
when the mind's well-centered,
when knowledge is progressing,
seeing clearly, rightly,
into the Dhamma.
Anyone who thinks
'I'm a woman'
or 'a man'
or 'Am I anything at all?' —
that's who Mara's
fit to address.