As long as you can reduce something to a pattern, it will work with a LLM. That's what they're great at, matching and recognizing patterns.

You might still do better with random moves. Depends on a couple of things.

First, a LLM is only as good as its training data. Depends on whether that data contained enough good moves that would work against a random button pusher.

There's also the question of whether the random pusher is human or not. Humans are not great at generating random data, we tend to think in patterns and there's also muscle memory. So I think the moves of a human random masher could easily fit into defendable patterns.

If the random masher is a computer I think it comes down to how well the game is designed, whether it rewards combos, whether longer patterns that build on each other have a large advantage over a series of completely random individual moves.