I think you will find that because you will be gaining a new Licence (FAA) you will need a Stsudent Visa to be issued as your C1/D1 Visa or a B1/B2 visa will not be sufficent.
If you are just doing a type rating in a sim only then you only need TSA (finger prints etc) for a new Licence Flight Safety informe me that I would need the student Visa also.
Check with your training provider everything else sound in order.
Good luck