According to stats posted by the Miniwatts Marketing Group and the annual Failed State Index, it appears that the OLPC project could help more than just the unprivileged children who receive laptops.
The Failed State Index gives each country a score off 1-10 based on 12 indicators. The higher the index score, the more unstable the country is. Comparing the index score to the penetration rate of internet usage based on population yields interesting results:

One potential argument could be that the states(countries) with low index scores are most likely states with poor economies, which would obviously effect the number of people who could even afford internet in the first place.
To test if the trend of increasing stability exists when countries with similar economies are compared, a similar chart is created using countries with I-5 indicator scores below 6. This indicator of the Failed State Index gives a score based on uneven economic development along group lines.
By comparing countries only with economies promising enough to sustain the costs of the infrastructures needed for internet, we get a better picture of how the internet truly effects ones stability.

As we can see, the upward trend still exists with countries with similar economies. Efforts by groups like the OLPC Association could end up affecting more than just the children the project aspired to help in the first place. Maybe some foreign aid should go towards building the infrastructures needed to get these failing states wired so they can stop relying on their corrupt or incapable governments and help solve critical issues themselves.
Besides, our foreign aid policy has proven not to work well in the first place, so we might as well try something new. I’m aware by simply wiring a country and allowing the citizens to have access to computers and the Internet isn’t going to magically increase their stability, but it would definitely help them in so many ways. Just think how much these technologies help us everyday and where we’d be without them. To say that this couldn’t help a failing state pick itself off the ground would be absurd.
All data used for this can be seen here