I think this is a neat idea if you live in a place where trans rights aren't protected or you feel really uncomfortable like in early transition, but it would be sad if people get the impression that you have to find a special restroom.
I stopped using mens restrooms once my presentation was good enough and I started getting wide-eyed looks of confusion/embarassment from men. I've never had a problem using a women's restroom in Europe.
A friend of mine still uses the men's at least sometimes even though she looks perfectly passable. I think it looks more awkward if you use your birth-assigned gender restroom once you start presenting/passing. It certainly draws attention to you in my opinion.