Stockfish vs a perfect player in the form of a 32 man EGTB that chooses randomly between moves that maintain a draw (assuming chess is a draw with best play) would probably draw some games.
A perfect player that purposefully chose between the drawing moves to make it harder on stockfish would probably win every game.
For example, even with the limited EGTBs we have, we've already uncovered forced checkmates that are 500+ moves deep. Sure engines are strong, but there are levels of chess that are completely beyond any imaginable future technology.
Still, some top engine programmers have estimated something like 3600... I don't recall exactly, but I remember thinking it was too low.
But, they're actually working in the field so I can't really argue.
The answer obviously has to be finite, since Stockfish would more than likely score some draws against it, and hence have a non zero score. My guess would be 4000 - 5000. Anyone have any more thoughts on this topic?