Yes, I know college students can absolutely do that. Understand that it has nothing to do with the conservatory. the professor is doing this in his/her own free time. My son’s professors have quite a few private students who are in college.
Now, professors always give preference to the conservatory students because those are the more serious, better candidates. So, if my son is not good enough then he will have no choice but to drop out of music altogether as he won’t find a good teacher to coach him.