Oh yes. Within the Fire Nation, their world has been tilted sideways after losing Ozai, and then now this non-bending girl that almost nobody has ever heard of is suddenly on the throne? (As regent, but still...) Surely there was a royal cousin somewhere who should have inherited. Or Zuko should have married one of the powerful woman movers and shakers of the Fire Nation, a general, or an admiral, or one of the governors. They don't get, or don't like that part of Mai's appeal as regent was that she wasn't any of those things, aside from the fact that Zuko loves her and is happy to marry her.

I can see that conversation happening, especially with somebody from the Southern Water Tribe or one of the Earth villages like Kyoshi, and Zuko explaining it, and the other person involved being like "This explains so much about why the Fire Nation is nuts".

This is very likely. They would want to present their marriage to the world as a done deal, and legitimize Mai's regency, but then they would also have to have a big public wedding to silence the people denying the wedding had happened.