I came in to GRU this past Thursday on a UA flight arriving nearly the same time as your AA option. Wound up saying in Sao Paulo because the client flipped the schedule on me so I didn't actually try a DIY connection but customs was super fast -- came out of business class on the UA flight and basically didn't stop moving until I got to the Immigration booth (the only person in front of me in the "foreigners" queue was long gone by the time I got to the end.

Baggage claim on the other hand was painfully slow -- maybe it's just UA's ground handler but it was probably 40 minutes before the first "Priority" tag came out (lots of non-priority bags started showing up at about 20-25 minutes). Even if it was a single ticket/through checked you do have to claim and recheck your luggage as part of the immigration/customs process