Not really;
Gpts are a class of text predictors. Ultimately they are ranked on whether or not the output is similar to the training data, text-wise. If the training data included a game then it may be able to play that game, but only if that game requires reasoning about entire words (because of tokenization, gpts can't reason in terms of letters, that's why they do poorly at crosswords for example)
On the flip side, alphazero is a class of networks that have a list of actions they can take, and a list of parameters they observe about the game (in chess: the board position, in other games: their position on screen, score, speed, etc). The model is then trained to take actions that maximize an actual hard value from the game, like winning a game of chess, capturing a piece, increasing a score, driving the furthest.
In theory you could train a model with the alphago method to do text prediction, but LLMs are called "large" for a reason, the input and output spaces would have to be the number of possible tokens (and at that point just train a normal gpt, it's much more efficient). Also in theory you could train a gpt to play games, but you're spending huge amounts of compute evaluating extraneous words in the input (the prompt) and the output (most words do not have anything to do with your game). on top of that, you're iterating over every word you generate to generate the next one, so you're doing multiple passes of this largely infficient computing, which means you're slower compared to a tailor-made model that can evaluate one situation once and give you a list of outputs to perform.
in this specific case it's a bit wierd because the input space for the alphazero model would have to be every word that can appear on the board, but the reasoning part is most likely not a problem given enough model size. since it's competing with a multi-gigabyte llm though, there is space to spare.