The fun part about this is that it depends on facts that nobody actually knows.

If you don't check ID then anyone with a list of registered-but-unlikely voters (or who registers unlikely voters ahead of time without their knowledge) could be voting multiple times and there is nothing to detect it. If you check ID then that doesn't happen as easily, but you still have no way to know if it would have happened in the alternative.

The closest thing to knowing would be if apparent turnout declines in response to checking ID, but a) different elections have different turnout anyway and b) even if you could detect a significant change, one party would then argue that it's a reduction in fraud and the other would argue that checking ID is reducing legitimate turnout, and you still don't know which one it is -- it could even be both.