Day to day working will probably be fine. Me and my cofounder live in different countries and sometimes only meet every 6 months, the rest is Skype. Share agreements (who owns what in the company) are pretty universal and they account for shareholders in other countries. But dealing with the tax office founders might need a tax id in the country the company is based. Thus legally for example I'm the only person allowed to sign many documents. That's my experience from Europe, I don't know much about US limited companies.
