Regarding the legal aspect, this idea isn’t new. There’s an episode on a lawyer TV show where two friends wanted to do this exact thing, and they won the case. After hearing both arguments the presiding judge said that once this kind of marriage is legal it is not the government’s job to investigate why two people wish to get married. After all, plenty of people out there marry for money or for show, but we don’t say their marriages are a fraud. As long as the marriage is legal the state does not feel the need to determine the motivation behind it. This is a fictional story but the show makes a convincing argument that such a ruling could occur and could certainly be defended.
As for the halachic aspect, I don’t know. I must say I am leaning toward maaris ayin, or chashad, because the Rambam says that if a man were to dress as a woman there would be chashad of this very issur, which is the reason behind the issur of lo yilbash. In my humble opinion, kal vachomer marriage.