My daughter was never interested in pursuing a dance career professionally, but she attended a pre-professional ballet studio and then an arts magnet high school as dance major, so there were classmates and studio-mates who did pursue dance careers, either by directly apprenticing to or joining dance companies or by going through BFA programs.
When my daughter was at Barnard, I know she had at least one classmate who danced professionally with a ballet company before coming to Barnard — I don’t know whether that was someone who deferred admission or simply applied later.
If my daughter had wanted to dance ballet professionally, then I would have encouraged her to apprentice directly to a company. Ballet is for the young – I think a young woman who goes for a BFA is setting herself up to miss critical years for her career. My daughter’s friends who got BFA’s were modern dancers, not ballerinas.
Are you talking about the college application process? (senior year of high school). There are no special requirements to get into a school with strong STEM offerings, other than GPA, test scores, etc. So she could just submit applications as appropriate – but nothing sould interfer with or prevent her from auditioning to dance programs in the same time frame.