Officially you need a visa to do " a course of training" if you are on holiday and the flying you do is ancillary to your being there officially you can do it on a visa waiver or tourist visa.
That being said it pays to not mention flight training of any description when going through the immigration.
TSA require you to register with them only if doing an initial licence or multi rating or instrument rating, as you hold a FAA CPL already you're ok to do the rotary add on.
Chester
