Interesting question. In NZ, if the aircraft says "XYZ going-around" that means into the circuit. If the aircraft says "XYZ commencing missed approach, climbing to (missed approach altitude)" that means what it says. If conditions are below circling minima (or other minima that may be peculiar to that ATC unit) the missed approach will be protected so there will be no issue there. If conditions are above circling minima ATC may require a visual circuit to be flown, but that is another story.
So it depends on what call the pilot makes as to what ATC will expect.