Oooops, my post got cut off before I could finish it!
I think I am the kind of person you are talking about! I am an English and Spanish major, but I love music and wanted to stay involved in college, so I played clarinet in Symphonic Band my freshmen year and in Basketball Band every year. I am even in a co-ed music fraternity, which helps me stay really closely tied to the music department even though I'm not a Jordan College of Fine Arts student.
I think you could definitely do this for vocal music, too! You could be in the choir, or one of JCFA's other ensembles like Madrigals or Jordan Jazz. There are also extracurricular options like women's glee club, Voice of Deliverance gospel choir or the wildly popular a capella groups - Freshly Brewed for women and Out of the Dawg House for men. I have had friends in all these groups whose majors range from music to computer science to international studies to physics. If you want to find out more about these groups check out the Student Organizations page or just ask! I would love to answer any of your questions. Hope this helps!