Apache..the simple answer is YES. A web site that might help you with the J-1 Visa is
http://travel.state.gov/visa;exchange.html While it does not specifically answer your question there it should give you some more information about the whole concept of J-1 Visas.
One thing that needs to be remembered is the fact that the US Embassy (or Consulate) issues the Visa. This means that no matter what the rules say they can deny your application for a number of reasons.
The approved school is responsible to sponsor your petition (IAP-66 Form) then it is up to the Consulate to approve you.
In terms of previous flight training...as far as I understand the requirement is for you to be FAA untrained. We have sponsored students in the past that had foreign ratings with only FAA PPL - some got the visa some did'nt but that again was up to the US consulate.
Hope that helps!