[AaronBrown]

I think you're basically right, but it comes down to the definition of "materially."

Suppose that people play any hand with two cards Jack or better, 20% of hands with one card Jack or better and 5% of hands with no cards Jack or better. Overall, that's 20.1% of hands.

The average hand has 0.62 cards Jack or higher, the average hand played has 1.33 of those cards, the average folded hand has 0.44. So each folded hand slightly increases the number of cards Jack or higher you expect in the rest of the deck, and therefore increases the probability that the remaining hands will be played.

After three folds, the chance that a hand is playable goes from 20.1% to 21.4%. Material? That's up to you.

Of course, this is oversimplified, but I think it captures the size of the effect.