Zero. None. Nada.
In fact, every Spring, there's almost always one or two players that have delays getting (legally) back into the states thanks to a visa issue. But the teams make absolutely sure that everything is legal and above board with their Latin America (or Japanese or Korean) talent.
This is true even for those having escaped Cuba: there's a process for establishing residency in another country and the State Dept. gets involved to give each one legal clearance before coming to the States.
Pro teams will have the best possible immigration lawyers making sure their players are properly documented. I also expect they have the best possible accountants available to make sure no player gets into tax problems. Sports tax is incredibly complicated because there are many jurisdictions, including in come cases foreign countries.