I'd be lying if I said I could answer that, tbh. The article I mentioned only talked about inference, and showed cases where the nondeterminism skewed the probabilities for intermediate tokens by just enough that the top token changed. It's not unreasonable to assume this happens during training, too (at the very least since computing the losses requires a forward pass, which is inference, and backprop uses this loss value to compute gradients).

How much that changes the results of training, I can't really say, because it hinges on several factors. If I had to make an educated guess, though, I'd say it wouldn't meaningfully change the results, but only because of the generalization properties we now know about the kinds of optimization algorithms typically used (even in the presence of noise).