It depends. Sometimes the fare rules require booking before a certain date. If that date is tomorrow, then you can't book it at that price tomorrow, even if held. Sometimes AA will ticket it at the held price anyway, but that is done as a favor, not because you have the right to it. Yesterday, there was an AA mistake fare available for a few hours. That fare said that there was a surcharge of $170 each way for tickets booked Dec. 1 or later. Mistakenly, it said that the surcharge was $0 for tickets purchased before Dec. 1. Any reservations held past midnight would incur the $170 surcharge each way. I would not expect that AA would be doing anybody any favors in that case.

When you hold it, AA.com says it will be held "up to 24 hours", not "for at least 24 hours". "Up to 24 hours" includes everything from one second to 24 hours.