Check in time doesn't count, other than if you or a travel companion are dropped from the wait list and need to update with an agent and that could happen to affect upgrade slots that become available.

For Load Factor Based Upgrades, LFBU offered at kiosks or check in counters time of check in could certainly affect your success possibility, because it's quite possible any possible LFBU offered when the flight opens could be taken up by the time later arriving passengers check in.