Unlikely. Very few employees in the US make exactly the minimum wage, which is why it's true that minor increases have close to no effect.
Keep in mind how many products are imported from third world countries that have poor labor standards & low wages. The current US lifestyle is heavily subsidized by this cheap labor. Additionally here in the US there is often abuse with illegal immigrants who make well below minimum wage & work in poor working conditions.
Intriguingly enough, without outsourced jobs from first-world countries, economic development in the third world would be even slower and labor standards poorer due to the lack of employer competition.
Are you implying a chicken and egg scenario whereby a third-world needs a first-world before it can become a first world? Going by that logic there should have never been a first world country in the first place. Who was the United States' United States?
Much of the third world is the way it is due to a history of instability, violence & repression, not necessarily a lack of well to do business men looking for an opportunity to avoid having to deal with pesky ideals such as labor regulation.
While it's great that Chinese have the option now of working 12+ hour plus days 6 days a week instead of going off & dying in a rice patty field, somehow I doubt philanthropic philosophy is the reason business goes to China.
This however is not applicable to every developing country, here in South America the majority of foreign companies are here because of the local market potential and not generally to produce here and send to another place in the globe, this happens mainly because of the existence of China and India that are more cost effective for this type of market than industries in South America.
Keep in mind how many products are imported from third world countries that have poor labor standards & low wages. The current US lifestyle is heavily subsidized by this cheap labor. Additionally here in the US there is often abuse with illegal immigrants who make well below minimum wage & work in poor working conditions.