The choice to do geo-targeting really depends on how diverse the markets are. If a page written for Peru won't attract potential students from Argentina, you may have no choice but to create specific targeted pages for each region.
I optimize English language websites for businesses within Latin America seeking clients from the US and Europe, so it's a bit different than your concept. However, some of these businesses also have/seek local clients. In such cases, having links from local (in country) English language websites has been critical to our success in gaining good rankings on searches conducted in country.