You do not need to register to transport unless the drone falls outside of fairly standard consumer level equipment. A military use type drone would need a bit of documentation and permissions. Registration is necessary when used. Just comply with air carrier battery transport requirements., and learn our airspace and flight safety requirements before operating.
Unmanned Aircraft Systems (UAS) Frequently Asked Questions/Help
I'm a foreign national and want to fly my UAS in the U.S. on vacation. Do I have to register before flying?
If you are a foreign national and you are not eligible to register your sUAS in the United States there are two ways for you to operate. If you want to operate your UAS exclusively as model aircraft you must complete the steps in the web-based registration process and obtain a "recognition of ownership." This recognition of ownership is required by the Department of Transportation to operate a model aircraft in the United States. Alternatively, if you want to operate your UAS as a non-model aircraft you must register your UAS in the country in which you are eligible to register and obtain operating authority from the Department of Transportation.
NOTE: at this time, the FAA's online registration website can only be accessed from a computer located in the United States or its territories or possessions.
That's for operation, not import. There's a distinction. They can pack it, but not fly it until registered. I do wonder how many of our own have failed to comply with the current registration requirements but fly despite that. That was not meant to be suggestive. Unfortunately foreigners can't access the FAA system out of country but perhaps calls to the FAA would provide a means to expedite the process upon arrival. Of course all that assumes their country has it's own registration process already in place.