As AA is dominant in USA-Brazil, it's possible that new AA will have to relinquish the CLT-GRU to DL or UA (I doubt GIG is at risk). And even if new AA gets to keep the GRU and GIG routes from CLT, I would expect to see them move to a hub with higher O&D to Brazil, like PHL or MIA.
As you probably know, the US has the opportunity to gain new air traffic rights for its carriers as early as this October with Open Skies between the US and Brazil arriving about a year later.
Because there is expansion of US air carrier rights to Brazil, it is unlikely IMHO that AA/US will have to divest rights but they will likely not be provided w/ any further rights.
IIRC, US' CLT-GRU service is supported by frequencies which are being leased to US from UA, which was not using all of the frequencies it had for several years. I believe the lease of the slots by US extends thru to 2015 at which time the US and Brazil are supposed to have Open Skies.
The real problem for the CLT-GRU flight is that there are no available parking spaces for normal morning arrivals and evening departures, which is the pattern for most flights in deep S. America. Thus, planes have to sit for the day; there are ramp areas esp. at GRU that are filled w/ int'l aircraft from around the world during the day. GRU does not have any more parking spaces which is why US has to arrive early in the a.m. ahead of other carriers and leave back to the US before the last wave of arrivals.
GRU is building a new terminal and Open Skies with the US is supposed to coincide w/ the expansion of terminal facilities and parking.
US probably will be able to eventually improve their slot times for CLT-GRU; the slot could be moved to another gateway but I'm not sure there is much value of adding any more flights from MIA-GRU - they operate up to 4 daily now.
GIG is in better shape with facilities and there should be no problem for other US carriers to expand there if they want to do so; thus, there is even less threat to AA/US' operation at GIG.
Other Brazilian airports have enough capacity to handle whatever flights other US carriers might add. The primary obstacle to adding flights at many airports is that many Brazilian airports do not have runways sufficiently long for nonstop unrestricted operations to the US.