His character arc will probably consist on leaving Oden's identity behind and building her own personality and perception of the self, which I assume are very fragile because of the childhood suffered and the lack of proper models when growing up.
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In fact I've been waiting for Yamato to make something actually crazy towards Momonosuke, the Scabbards or whoever, because I just can't see it as a gag no matter how theoretically funny this should be. From day one, the vibes coming from him have been quite weird.
I find the trans debate to be legitimate with Kiku, who is way more clearly depicted as such, but in Yamato I can't help but seeing a person with important problems on the development of their self and I'd expect her to see herself as a woman from the moment she leaves the Oden impersonation behind. But I don't think this changes the fact that, so far, every character has referred to him as a man, so I will stick to that for now.