Absolutely need to go through immigration, wait for your bags and go through customs at GRU (your port of entry into Brazil) just like you would entering the U.S. After immigration you can shop at a large duty free store. To go through customs you don't have to fill out a form unless you have something to declare, though you could get pulled out of the "nothing to declare" line for inspection, even at random.
Having your bags tagged for BH will make the connection easier at the transit desk (see below) and keep you in international baggage weight limits for your domestic flight. So UA should tag your bags for your ultimate destination, even though you will make a connection at GRU (and have to get your bags, etc). I don't see it making any difference if Azul puts their tags on in addition to (or in place) of United's.
The transfer desk is, as stated, after customs, in the main hallway outside the security zone, at GRU. Last time I was there, there was a sign for Azul (plus lines for TAM and Gol). Here you'd hand over checked bags and get your boarding pass for Azul (assuming both flights were purchased together).
My wife has flown Azul and quite liked the service.
Last edited by SoCal; Oct 11, 2014 at 8:38 am