In Florida, the absentee ballots are the FIRST ballots counted, generally on the day before the general election. They are opened, counted, and certified, with poll watchers on hand, in secured rooms.
This method or similar methods are common and typical in most states. Then the early votes, where allowed, are certified, often again before Election Day. That gets all decks cleared for the Election Day voting, and the review and certification of the few absentee ballots that trickle in on Election Day.
Yes, all votes are counted.
What usually doesn’t get counted are the ‘provisional’ ballots. Most of these do not get counted as they caster cannot be certified as a registered voter.
But I think many of us remember reports from Bush v. Gore in 2000 that some ballots in Florida would never be counted.
I don't remember which ballots were allegedly assigned this "not necessary to be counted" status, but it might have been the military ballots that came in from overseas. There was a lot of outrage over this iirc.