I don't recall hearing anything about that. Though, I have heard that groups/clubs may be allowed to create Live tourneys at some point. I would assume those would allow variations.
Tournaments?

That would really be too bad not to have them scheduled every day like normal tournaments. I really think the best way to enjoy these variants is a tournament. It would absolutely be the way to get people playing them as well. Chessnetwork's king of the hill tournaments he films from lichess look like a lot of fun and I think chess.com should be all about that with king of the hill and 960 and 3 check, it would be great.
Has Chess.com said whether or not they are going to make tournaments with these variants? I really hope so.