Actually Lola, if I were committed to riding a scooter to and in South America, I don't think I'd take either a GTS250 or a GT200, though I have owned both and both are fantastic scooters. I have 15,000 trouble free miles on my GT200 and rode it up to Canada and back from San Diego.
Having said that, if I were going to ride in SA, I'd get a '70's Vespa P200, rebuild the motor, suspension and wiring, get a BBQ rack, and head off into the sunset. It carries a spare tire under the cowl ready to go, so you don't have to carry an extra wheel with a tire on a rack. Parts are available just about world wide, and I'll bet there are more P series Vespas in South America than any other model. Not only that, if you do break down somewhere and need an engine rebuild, it can be done in a matter of hours on the side of the road, if necessary.
The BBQ rack and a front rack would allow you to carry plenty of gear. One drawback: small gas tank, so you'd definitely need a rotopax or two. I'd think about putting a Rally style gas tank in the scoot just to have a little more range, and carry some cables with you.
I'm rebuilding a P200 right now, and decided (with the help of a friend) this morning that the P200 will be my Pacific Northwet Cruiser, garaged at my daughter and son-in-law's home near Seattle. That way when I'm up visiting, I can hop on the scooter, and avoid rental cars, and can easily make the trip up to Vancouver Island to see my parents.