I was thinking along the same lines, but not familiar enough to know how a failure in that component would result in the brakes applying themselves. I lean more towards the booster not sealing up like it should (maybe contaminated by a failed vacuum pump).
If you pull the vacuum line off the booster and the brakes release at least we're in the right ball park.
The vacuum pump to my knowledge is always running, I don't recall ever seeing a clutch on it, seems to me it is either creating vacuum or not - it SHOULD be creating vacuum at all times (the problem would be present at all times too).
I suppose one could try to pop the belt off the vacuum pump to rule it out of the equation.