The last 4 or 5 round trips I have done between LHR - LAX or ORD -> LHR I have booked in discount economy and then called up AA to use miles + copay to upgrade to Business (C class inventory). Every time I have been put on the waitlist but the upgrade has always cleared for me. A couple of times the upgrade cleared a couple of weeks before the flight and sometimes it only clears a few days before. The last time I flew to LAX the upgrade hadn't cleared by the time I got to the airport but all I had to do was ask about it when I checked in and they processed the upgrade for me at the check in desk.

The first 2 times I did this I was platinum and the last few times I have done it as gold so I'm not sure if you would have the same luck as a non-elite member. But I think I remember reading somewhere on FT that miles + copay upgrades are processed before EXP SWU's on int'l flights... not sure if that's correct though.