It's possible to measure this effect indirectly. This
link gives rank statistics for board cards in a large sample of on-line play. They are very close to what you would expect from a random deal, but there are slight discrepencies that are too large to be the result of random chance. There are too many low cards and not enough high ones. This is because when there are lots of high cards in the hands, it is more likely to progress to flop, turn and river.
However, as you say, the effect is much to slight to help in real Poker.