I've certainly missed flights from DFW to ORD on account of AA delays, and been confirmed on later flights of course, but my guess is that if they even allow it you would be going standby, unconfirmed, unless you want to pay the ticket change fee.

Luckily there are plenty of flights to ORD, but then again it's the holidays, so if you were elite it would help ease your mind about getting a seat.

But...I would just call American, tell them what you are going to do, and ask them if you can go standby on a later flight. They won't red-flag you for it, and you'll get the right answer for sure, and know exactly what to do or not to do.