Well, no.
Even if it were true, the argument would still have to be "I have a ladybrain and that makes my male body actually the same as your female one in a deeper than physical sex way", and that is still a big (I would say indefendable) claim.
The reason we have female only supports is because people with female bodies were marginalised or at risk. Having some sort of ladybrain structure in a male body doesn't put one into the catgeory of people with female bodies.
Saying a "womanlike" brain structure if found in a male mind means that man is actually a physical female is like saying if a cyclist drives a car then the car is actually a bike and it's fine to use it in cycle lanes, race in cycle races and so on 😂 The issue is not the the cyclist isn't a cyclist, it's that the car is not a bike.
So end of the day, even if it were true, it still wouldn't justify what trans women want from women.
It's just another manipulation, an attempt to imply that if you don't accept TW as women you are somehow base, unable to perceive beyond a simplistic physical object to a deeper realm of mind. Emperors new clothes. Confusing mud being thrown around to justify a demand that if was made in simple language - "I am a man but I feel like I think women must feel so I want you to pretend I am one just like you" no one would consider reasonable for a hot second.
At best it might mean a little more sympathy to why the demands get made (although as I said on another post, the "womanhood" expressed by some trans women is very hard to reconcile with my experience of being female and sometimes downright offensive, so the idea that it's stemming from some sort of genuine mental commonality with female people is - unconvincing).
What it might do if actually real is bring about a more subtle understanding of personality. Maybe we'd start to see BrainFeel as something meaningful and maybe have services/supports tailored to that. But that would be something aside from sex, not a replacement for sex or a reason that physical sex, that has been a significant factor in how we humans treat each other and see ourselves, is suddenly magically not going to be noticed.