My understanding is that you do not need TSA clearance if you already hold an FAA commercial. You need the clearance if you are substantially increasing your skill level, such as with an instrument rating. An ATP is supposedly proof of skills that you already have.
Allatps do not issue you a visa. They are expecting you to read between the lines and go on a tourist waiver and just show up.
While some schools may give you the I-20, a consulate may not issue a visa for such a short term study program. It is one of those things that in any other industry you wouldn't need a visa due to the shortness of time needed, but because it is aviation everyone thinks you should have one. So technically you don't, as it (should) be less than 18 hours, but you could end up with all sorts of trouble from customs and immigration.
Good luck!