Yes, I think that, subject to minimum wage laws and fair labor practice laws, you can make absolutely anybody work a week for free as a condition of holding a job.
Of course the minimum wage and fair labor practice law exception completely guts the concept, since it would be illegal under both to force somebody to work for free for a week.
Of course students are not under such laws, they being students and all, so Columbia can legally force them to give 40 (or presumably 1000) hours of pro-bono service to "approved" (i.e. liberal) causes.
And of course people so forced resent it and don't forgive it or forget it.