Us patents protect inventors in the US, not in foreign countries. That is why for important products companies will file patents not only in the US but in the European Union, Japan etc. as well.
If your offshore company does not do business in the US, only in some country like Bhuthan or Cuba that does not have patent treaties with the US you will probably be fine.
On the other hand if your goal is to do business in the US infringing on a solid patent owned by a company like IBM or Microsoft, simply having a company overseas will do little to protect you.