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.
Visited Ireland last year. Fantastic country. Drove around the whole island on a 10-day road trip. Would definitely do it again, and it's sad this orange shit stain will make life harder for my Irish brothers and sisters. I hope the people of Ireland find another outlet. America is trash and it doesn't deserve you.
I have no expertise, but I'm guessing that the world will adjust faster than expected and just start trading more with each-other and leave the US to rot on it's own.
Maybe they shouldn't have been offering <2% tax rates to corporations? Ireland's 'Fuck you I got mine' tax laws are a net detriment to the rest of the world, it takes away tax dollars from other countries that could have been used for public services.