I studied 'cello with an internationally famous full professor while I was in high school. I would take a train down to New Haven from Boston several times a month and spend the day on campus for private lessons, ensemble, and master classes. It was mostly graduate students, but there were a few undergrads. I would think from this that there would be some flexibility depending on the seriousness and talent of the student.
@Hunt, I think it’s very difficult to go to a University of Yale’s caliber and maintain the kind of single handed focus that is necessary to develop in music performance to the same degree as one would at a conservatory. I went to Stanford, and my brother (violin) went to Harvard, both with the intention of keeping up our music performance, and we both found it quite difficult. There are places like Oberlin and Indiana University with strong performance departments, but they aren’t Yale from an academic perspective.