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I have no doubt that AlphaZero could easily do most Chess variants. My previous posting in this thread was a reaction to Greg's remarks on Stockfish. There boards larger than 8x8 would indeed be a problem. For AlphaZero, not at all.

As to the maximum capacity in terms of board size: I am sure there is one in the current system. But I am also pretty sure expading those limits would just be a matter of recompiling the software, and perhaps throwing more hardware against the problem. Note that the effort on Chess used overwhelming computing power by doing things in parallel that could just as easily have been done sequentially. Like generating the self-play games. As a result it took only 4 hours for the machine to teach itself to play Chess at the 3000+ Elo level starting from just the rules, rather than 2 years.

Everything will just get slower if you would be trying larger games. Bigger doesn't always mean more complex, though, and I can imagine that there are large games that do not need much finesse to play, and still can be learned in a small number of self-play games. (I imagine something like Checkers on a very large board.)

Game play by the trained machine would also become slower if the number of moves per typical position goes up. This will expand both the game tree necessary to see the essential tactics, as well as the neural network needed to guide the search. But of course all other methods to play the game, such as human thinking, will suffer similarly.

There is one problem: AlphaZero will be able to master any given Chess variant quickly, but after that, it still cannot tell you how it should be played. Even for simple things like piece values, you would have to reverse-engineer those from the neural net, by presenting it sets of positions with material imbalances, and looking how this affects the win probabilities that it predicts on average for those positions.