No.
The prostitute who anoints Jesus' feet in Luke was a different woman. The mix-up is a medieval conflation.
Besides which, the idea that that automatically constitutes 'making oneself available' in that sense, or that it's somehow more reasonable than not to expect that Jesus would have taken advantage of that even if she had, strikes me as...concerning, extremely so.
But why? I mean, whether it be a man or a woman that he would be attracted to, why would a deity who wants to be human reject that aspect of humanity?
That's not what's concerning. 'Made herself available?' That's really how you want to word this?
It's all the same. I find it odd that someone would think Jesus would reject her out of hand if he found her attractive. And if not her, then maybe someone else. That's just how it works.
You don't get why a monotheistic religion would be interested in presenting God as in some sense neuter, human form or otherwise?
No, not at all. I think it would be the opposite.
But either way, this is religion, so you and I are perfectly free to project onto God whatever characteristics we see fit.