Shouldnīt be a problem with Alpine Aviation, as they are an approved SEVIS school and sell their FO program as an "advanced qualification program". Means you are undergoing a flighttraining and you can log your time on the controls as PIC under part 61.
Just checked on
http://www.ice.gov/graphics/sevis/pd...vedSchools.pdf
couldīnt find eaglejet or Ameriflight in there, so wonder what Mr. S.H. is selling there.
cheers