I'm having trouble understanding the question too, I think maybe because I just didn't share that experience so I'm like, "huh?" If I understand it correctly, I would say no that wasn't something I ever noticed myself doing.
Nowadays, I look at some women as role models for sure. I see how they are and think, "that's a good way to be." I see that as being a pretty normal thing to do.
Before I came out, started transition, etc. I would see plenty of women I felt I had things in common with, but I didn't really ever give it too much notice. Like you, I was fully aware I would fit into society better as a woman. I would look at men in media and society at large to see how I was supposed to act, because acting like a man didn't come naturally. I was terrified of growing up and having to be a man because I didn't think I could ever learn to be like that. I feel I'm talking more about gender than gender identity with those examples, but maybe that's what this question is about. I don't feel gender roles affected my gender identity, but I think my gender identity made me feel uncomfortable in the wrong role.
I dunno I'm just throwing a lot of things out there in case any of them answer your question.