Is it possible to define a state of zero absolute angular momentum anywhere in the universe?
Angular momentum does not change unless a torque acts upon a body. So your question is just whether the torque on a body could ever be exactly zero. The answer is of course that it can be arbitrarily small but we can never be sure it is exactly zero.

More interesting questions would have been "does the CMB exert a torque on an object?", or "is it possible to define a state of zero absolute angular momentum?".