Covers are posted periodically and I'm not aware of any issues that have come up with them beyond the group's general leaning in taste toward original material. Since the clinic is essentially an educational entity I don't think copyright enforcement is much of an issue to worry about.
I wouldn't think there would be a problem. You're not making any money from it, just asking for help in the mixing area. If, down the road, you include your version on a CD release then you will have to get the mechanical license for permission to use the song.
But again, I think the original artist will only complain if you are making money from their copyrighted material... OR if they really hate your rendition.