As a Gold, I usually try to check in online right at T-24 in order to get the free MCE seat, so I usually set my phone alarm for a few minutes earlier than that. On my last two flights, I've notices that the Check In link on the AA Android app has become enabled early, once at 24:01 and once at 24:02 before scheduled departure.

I've checked in then and it's worked just fine.

Unfortunately, even after checking in, the MCE seats are still paid until 24:00.

Check in time doesn't matter for much anymore, but I think it's still the tie-break for standby lists, so maybe this tidbit will be useful for someone planning to do a voluntary standby (or fearing weather cancellations).