If a pilot has been told to "expect late landing clearance (reason)", in my experience, the crew will decide the "go around" point/level taking into account the prevailing situation, vis, w/v and the reason landing permission has been withheld.
A modern aircraft may execute a go around from 50 odd feet or less and not touch the runway. So a controller may give a go around just short of the threshold (if that is a safe option in relation to the obstruction)...however, consider the pilot's "reaction time" and aircraft's inertia!