Legally, you can't, and there's a good chance they'll ask for proof of address.
Travel regulations are completely different in the USA compared to here (they notably have the option to renegotiate the cruise price if it officially drops).
Plus, if you manage to book it, good luck if there’s a problem (cancellation, itinerary change—it can happen) because hardly anyone will help you. The US call center will tell you that you shouldn’t have booked through them, and the European call center will also brush you off.
You might save some money, but for me, it’s not worth the hassle—the protections just aren’t the same[;)]
A chaque escale une nouvelle histoire - Agent de Voyage spécialisée en croisière