To register an aircraft on the American registry the aircraft owner must be either a US Citizen (natural person, body corporate, trust) or a Resident Alien (or technically a foreign controlled corporation if the aircraft spends 60% of its flight hours per year in the US and the foreign corporation lodges a declaration to that effect - but this is not relevant to you).
An un-registered aircraft is not legally airworthy.
Ergo, as IO said you can't legally operate (or as I said, you can't own it) depending on your perspective.
Which is why I asked who was buying it - on the assumption it was not going to be just some dodgy mates but a reasonably defined structure - that would not take unreasonable risks with their airplane - because as a foreigner operating on the US reg - it is not your airplane (you may be the beneficial owner but not the actual owner).