HD - the funny thing is we can go on all day because we use the same terms but they mean different things. Qualified to the FAA is the same as certified which is synonymous with licensed in most of the rest of the world.
If you are asking about ATC school, every ATCO in the FAA has been to the FAA academy for ATC training, with the exception of a very few that were hired directly from the military or DOD. They were all prior controllers that went thru the military schools. Even the college graduates with ATC academics and simulator training have to go thru the FAA academy and pass a very tough program.