if you have a valid address in the US and you fly a drone, citizen or not of the US you should register or you could face a fine if you get caught. Better ask. However, if you are an illegal alien in hiding you better not fly at all and I mean that with respect.
Yes, if you come to the USA (on vacation or otherwise) with a drone that meets the requirements you must register it. Use the same online method that we all use.
Q11. Are non-U.S. citizens visiting the United States on vacation or for drone competitions required to register?
Everyone, including foreign nationals and tourists, who operate a UAS for hobby or recreational purposes outdoors in the U.S. must use the FAA's online registration system. These non-U.S. citizens or non-permanent U.S. residents will receive the same registration certificate as U.S. Citizens or permanent U.S. residents. However, this certificate will function as a "recognition of ownership" document. This document is required by the Department of Transportation for foreign nationals to operate legally in the US.