As others have said the only correct answer is yes but .. .. ..
you can get BFR done in the UK before you go. This has a number of advantages, not least a saving of time and worry when you arrive for your holiday. If there are any issues on which you are not current (and in particular you may find you are rusty on American air space) you can get these sorted out before you go. Do remember there is a theoretical comment to the BFR unlike in the UK and you can fail.
If you take this route you will only need a check ride in the States to satisfy the instructor you are competent on type.