Assuming an infinite amount of computing resources, would the minmax algorithm always win in chess?
By definition, minmax chooses the move that results in the best possible outcome if the adversary plays optimally, but within the bounds of what the evaluation function takes into account. More precisely, minmax results in the best outcome that can be guaranteed no matter how the adversary plays, as long as the adversary's behavior is no worse than what the evaluation function predicts.

If minmax searches on the whole tree, then it never calls the evaluation function, and therefore it models the adversary perfectly. So in this case, minmax achieves the best guaranteed outcome that can be guaranteed against an arbitrary adversary. This is true regardless of the game.

For chess, there are three possible outcomes: win, draw, loss (from best to worst). We don't know what the best guaranteed outcome for each player is. But whatever it is, if you can run minmax on the whole tree, you'll get that outcome or better (the outcome can be better if the adversary plays suboptimally). Of course, this is only practical near the end of the game when there are few pieces remaining in play.