Yes, but the Irish part of the company does business in the EU, while the American part does business in the US. For example, Google Ireland isn't exporting phones to the US. They're made in Taiwan (or wherever) and imported to the US by Google America. Businesses set up this way so that the US can't impose taxes on their EU business.
(That's my understanding, anyway. It might not be 100% accurate.)
The challenge is usually repatriating this funds back to the "home" country. However, many multinationals have been quite happy leaving the profits outside of the "home" country for additional foreign investment in those regions.