With infinite power, we could trivially recursively check every board state for winnability, and gradually work back towards knowing the winnability of the opening position.
At that point we would be able to definitely state whether perfect play leads to a White Victory, Black Victory, or Draw.
I don't know what the maximal tablebases currently are, but it seems like if you have a perfect tablebases for N-pieces, then exhasutively testing a single N+1 piece position shouldn't be that hard, and you would in the process also cross out a bunch of other N+1 positions. So the difficulty isn't specifically in evaluating positions at the next N, it's merely "there are a lot of those, and exponentially more of the next layer".
But we also have a LOT of brute-force computing power available.
How long would it take Google or Amazon to add another layer to our endgame tables, if they chose to?
How long would it take to just SOLVE chess, if humanity chose to?