bquinif's answer is pretty much on spot.

LA flies SCL-GRU-GIG and GRU pax are cleared in GRU while GIG pax stay inside to get cleared in GIG.

RG used to send all flights to GRU and once in the sterile area they would send pax to GIG, CNF, CWB, POA, who then would clear immigration and customs. This was most efficient to RG until the Fed Police got annoyed at how messy was with RG's controls that used to make having pax left out and eventually getting into the country uncleared.

Currently Government makes Varig pax deplane and clear all pax at their first point of entry - Immigration and Customs now get done in Sao Paulo.

Eventually pax might board on an international flight for operational reasons, but with all documents and luggage having been screened and duly checked.

If the later is your case bear in mind that if you take an international flight on your way to Rio you'll be secondly screened through immigration (on your way out of GRU and way in at GIG - no problems, you have been cleared in GRU) but customs might decide to check all your luggage once again as you've been in contact with unscreened pax.