No - you would carry out the Go Around at the time of the ATC request. There is no requirement to continue to minima if you or ATC require the discontinuation of the approach.
'SevenStrokeRoll' does raise an excellent point though; At airports like LaGuardia (New York) or Midway (Chicago), where the level off altitudes for a missed approach are typically low, some thinking is required. In this case I prefer one "click" on the TOGA button. This provides a more manageable rate of climb. The obvious safety caveats being - VFR, Day, no obstacles and a non critical altitude at which the missed approach is commenced.