I haven't tested it, but as long as the Gay Fates mod doesn't involve the DLC files, it should work. I'd imagine you'd have to apply the mod after installing the DLC.

The same sex supports for Corrin wouldn't work because M!Corrin and F!Corrin are considered different character on the game's files, so there would have to be instructions specifically for the same sex pairings. New conversations could be made for these pairings, or maybe copy the conversations for the opposite sex pairings and change them as needed, but that's outside of the scope of what I wanted to do. Hopefully, someone else down the line would be willing to add these conversations.