No you cant get your visa while you are out there but if you are that keen you can choose your school get them to issue your I 20 while you are there and book a visit to the u.s. embassy in the bahamas. you can get regular cheap flights from Miami to Nasua. They will interview in the morning and issue your visa the same afternoon. A few of us who studied out there had problems with our school and did this it was a fairly painless process. As for TSA hold ups I have no idea where that comes from we did our TSA paperwork after we arrived during the first couple of weeks of ground school and never found it an issue.
I have been at a few different schools during fur different visits there and done my atpl ground school there p.m. me if you want my opinion on any of it because believe me there are many problems with various schools that only become apparent after you are there and you already have your visa tied to a specific school. really depends on what training you want to do.