From Wikipedia:
An often-cited example of factor price equalization is wages. When two countries enter a free trade agreement, wages for identical jobs in both countries tend to approach each other. After the North American Free Trade Agreement (NAFTA) was signed, for instance, unskilled labor wages gradually fell in the United States, at the same time as they gradually rose in Mexico.[citation needed] The same force has applied more recently to the various countries of the European Union.
Apparently, not only CAN it happen, it already has.
I had no idea, but I'd like to go to college and major in Econ. So, helping you taught me something. Yay!