Birthright is telling me that a 14 day trip to Israel with their US seminary would make them ineligible for a Birthright trip but their website seems ambiguous at best.
University Trips
Applicants who traveled to Israel after turning 18 on programs including gap year programs, to attend University or study abroad semesters/programs, yeshiva & seminary, as well as any program under the umbrella of Onward Israel or Masa are not eligible.