You need to check with TAM and UA in advance. The fact that your two flights were booked separately could make a difference and you may have to get your bags at GRU. We've transferred from TAM domestic to UA (and other) international flights at GRU a few times, and in each case our bags were transferred, though we still needed to exit security and go to the UA check-in desk to get our boarding passes, then go through airport security and passport control before going to the gate for our international flight. But our flights were booked together. You want to confirm your sitaution in advance. Presumably you'll know when you check in at GIG, by whether the TAM agent tags your bags to just GRU or all the way to ORD. Hopefully you won't be limited on the first flight to the very low domestic flight baggage weight limits (you wouldn't be if the flights were ticketed together, and may not be in your case).

At least ask TAM at GIG (or in advance) if they can tag your bags to ORD. We were able to do something similar when traveling on two separately-booked tickets from DCA to MIA (on AA), then MIA to Brazil on TAM (our bags were transferred, but we had to get our TAM boarding pass at MIA). Remember, even if your bags are transferred you will almost certainly have to go to UA at GRU to get your boarding pass.

I'd phone TAM and UA in advance just so you know.