I have this lock,
Sure, in fact I removed the bracket a few times trying to find a non-awkward mount location on my frame before outright throwing the bracket away.
Just stick an allen wrench into the strap locking cylinder and twist Hard backwards.
I wouldn't reccomend this for daily transfer between frames though, since you're going to be wearing down the ratcheting teeth on that bracket each time...
In fact, just throw away the bracket, its heavy and gets in the way and is ridiculously over-engineered for what ought to be a simple plastic strap and bolt. Keep your U-Lock stuck in your rack.