The whole non-binary thing is tiresome in the extreme. Tilly disclosed it to Marten because she knew about Claire from the dossier and that it would touch a chord with Marten. The same way Tilly thought she was buying trousers and a bag in Hanner's favourite colours. It was a deliberate attempt to curry favour and get under her skin. Would you trust someone like that?
She is as manipulative as hell.
Your misuse of their proper pronoun aside; your argument doesn't track.
Look, I'm as anti-Tilly as anyone here. I didn't think the stalk-y intro was appropriate. I think they're a shit character who brings nothing new to the story and in the "bringing of nothing", actually, drags the comic down by wasting time on them that would be better served on other characters and their story lines. That said, I would be absolutely BLOWN AWAY if we were headed down that path.
A character that's pretending to be non-binary to ingratiate themselves with the friend of their new boss? No. One, I don't see Jeph being ok with that in any capacity(I don't claim to know him or be psychic but after reading the comic for so long and watching all the care he puts into the handling of sensitive topics? No, don't see it). Also, two, why would such a little detail mean one thing or another to Martin? But..hmm..ok, for the sake of argument, let's say for a second, it did. That Tilly being non-binary helps them get Martin's friendship, somehow. How would that help them if Hanners decides to fire Tilly? It wouldn't. And while Tilly may be a bit....."much", I don't think even they would have the cognitive dissonance to think that it would.
Finally, buying pants and a bag in what you believe are your boss' favorite color is no where CLOSE to being the same as, "I'm pretending to be non-binary to curry favor." It's just not.