I actually haven't seen a hand that would have eventually held up as the best one not count towards the later sequence, so I haven't witnessed any high hand actually go to waste yet, if I'm right. But I've held quads once or twice, as well as a bunch of full houses when the time period has ended, only to see that a flush or something is still in the lead after like 2 minutes. Saw another player have a straight flush in one of those ongoing hands when the timer switched, that didn't end up on the leaderboard. At that point I still figured maybe he's geographically not eligible for the promotion. But since then, for a while now, if I've held or have noticed a full house or better during a sequence switch, I've started to check if it shows up on the "leaderboard" and it never seems to.
If you have tracked what hands were in the lead after x minutes, I'm sure I can dig up some hand histories that didn't hold top place in the beginning of a 20min sequence. But I don't have a hand history that would show a better hand than the hand that ended up as the best after the full 20 minutes.