I guess the word "theorem" is a little strong, since it depends on the real world. I stand by the statement that it's literally impossible to decide this in practice. If we are allowed to say in a few lines of code you could formally compare any chess engine to a theoretically optimal one, then obviously it is possible to decide by just comparing.

Without being allowed to compare a given engine to a theoretically optimal one which is based on brute forcing the full game tree, and being careful about the problem statement, I suspect it would be possible to prove something along these lines

I would argue something like: "Gods evaluation function" takes as input a chess position and returns whether the position is a forced win, lose, or draw. The rules of chess are so complicated that to go from a continuous evaluation function to a discrete one like that would require an infinite number of steps (this last statement is the one that needs to fleshed out)

I will stop calling it a theorem until I remember why I started calling it that. This situation exists in many non-linear optimization problems, a subject I find really interesting, and in many cases in practice there is no way to decide if a given solution is optimal. For some reason I thought there was a theorem in non-linear optimization theory that was directly relevant here