I don't know if WWE or WCW ever ran events in South America, but I do think that the popularity of mainstream global pro wrestling promotions in that part of the world will come if and when wrestlers that are actually from there start to become relevant on the international stage.
You can point to a ton of Japanese pro wrestlers that had a decently popular run in North America. You can name a ton of Mexican stars and probably some Puerto Rican ones. You can name a lot of great Brits.
How many Brazilian wrestlers ever made it big in WWE, TNA, NJPW, WCW, ECW, AAA, ROH, Noah, AWA, NWA, CMLL, or AJPW? How many Colombians? Peruvians? etc.
Until these countries get their own Davey Boy Smith, Pedro Morales, Bret Hart, Rey Mysterio, or Jushin Thunder Liger they're not going to have a lot of reason to follow a wrestling promotion 1 or more continents away.