Hey, Im just back from 1 year in South America. Your question depends very much on what kind of cyclist you are and what coutries you want to visit. I rode from Santiago de Chile to Caracas/Venezuela. In Chile and Argentina (not the southern cone) you can pretty much stay on the paved roads. But if you are thinking in cycling the Andes and the Altiplano in Bolivia and Peru you will be definetly better up with a mountain bike. However, I made a girlfriend down there and I had to make a few compromises
we skipped a few parts by train or bus when it was just getting too hard. Especially in the Peruvian Andes the unpaved road can get really rough. You wouldnt be able to do that without a mountain bike. On the Altiplano in Bolivia u have sandy and corrugated sections. Anyway, we've also met guys on touring bikes, so it seems to be possible somehow. One thing is for sure: if you like to get off the beaten tracks and if you have time (means if you dont just want to make it from north to south), you'll find it interesting on side roads and you'll enjoy a mountain bike.
If you have any more questions, just ask or have a look at my website, too.
http://www.ekkis-world.de/index-engl.html