Indeed, calculating "performance" is very tedious. However, in the context of the OP's original question, we are most interested in turn radius. Without knowing the specifics of the airplane involved (limit G, power available, etc), and knowing the OP is not an experimental test pilot with access to all the associated resources, simplifying assumptions serve well.
The link posted by BOAC gives enough information to get a handle on the problem. Using a few simplifying assumptions and/or example data (as I did above) serves to quantify the problem. Using numbers typical of light GA airplanes and disregarding vertical maneuvering, we now know that we can cut the turn radius by a factor of 2 by reducing airspeed from [the vicinity of] Va to Vy. Also, since excess power is maximized in the vicinity of Vy, that power can be put to good use in developing G.
OTOH, we also found that dropping flaps may not be a good idea in light GA airplanes, because the reduction in G available likely more than offsets the reduction in minimum maneuvering airspeed (which may be on the order of only 5-10 knots).
OTOOH, dropping flaps in a transport category airplane significantly reduces maneuvering speed (e.g., by 80+ knots in a 747) while only reducing limit G from 2.5 to 2.0, thereby becoming a distinct advantage in reducing turn radius.