Yes, as an AA Platinum member you may standby for a different flight on the same day free of charge. The process is the same, whether on a paid ticket or on a redemption ticket.
Do not simply no show. If you do that, your ticket will be cancelled when you miss your flight. What you should do is call the AA Reservations desk, and let them know that you intend on standing by for a later flight. What they will do is cancel your original flight and list you for the one you want. When you get to the airport, you will go to a check in agent at the counter, and you will receive a Priority Verification card. You will use that to get through security. Then report to the gate or the Admirals Club, if you have access. The AC agent or GA can keep you updated.
Again, this process is the same whether you are on an award ticket or a ticket paid with cash. Keep in mind that there is the possibility of not clearing the flight, and all subsequent flights (well, there is only one more, that gets you into BOS at midnight). In that case, you will be stranded at ORD until you can clear.