There is an audition that you'll have to go through. Being able to read music is a plus but depending on your talent, its not insurmountable.
I will admit that getting in is pretty competitive. I think there are only about 25 members right now. Gen. Johnson has given them LOS status, so starting next academic year, they'll be treated like an IC sport & get out to "practice", so I suspect that competition will be even more fierce. But, you won't know unless you try out!
Keep in mind that there are also Catholic and Protestant choirs you can join with no audition (and I recommend it!) If you really enjoy singing, those times will be the most serene and relaxing times for you.