Which prop-shaft?
I've had the universal joints (UJs) fail in mine before, both front and back, and the noise/vibration can be quite dramatic!
I've driven mine in diff-lock with only the rear prop-shaft and it seemed fine - a bit more "clonky" than normal, but fine.
I've never tried driving with the rear prop-shaft removed, though - theoretically, it should be fine, but I don't think I'd fancy it...
When my UJs failed, I replaced both compete prop-shafts, but I think that was an expensive way of fixing it - I'd have a look at overhauling/replacing just the UJs if I had to do it again...
Good luck with it