First, what do you mean by "effective?"
Unboosted controls, which were used on almost all WW2 fighters, can require too much force to deflect far at high speeds, but this is a problem that tends not to afflict rudders, because legs are much stronger than arms (to confirm: get a number of people to try doing a one-legged deep knee bend, then try doing a one-armed pull-up. I predict far fewer people can do the second than the first) and because the rudder is used to counteract adverse (or proverse) yaw from the ailerons (airplanes don't turn with their rudders; they turn with the ailerons), destabilizing effects of power, and to deliberately slip the aircraft.
Controls also rely on the force of the air to function. As aircraft speed up, the force on the aircraft from the air increases. Since the amount of force a control surface can produce depends (roughly) linearly on deflection (the angle it makes relative to its normal location) and by the square of the airspeed, more deflection is required to generate a given force at low speeds, and it's possible for the amount of deflection to simply be too small to produce enough forces at low speed. Designing unboosted controls to work well over a wide speed range is difficult, which is one reason modern combat aircraft almost universally use irreversible, .i.e., no force feedback between control surface and stick, hydraulic controls with artificial feel.
So, to directly answer your question: the rudder on a Spitfire would be effective at high speed. The pilot would not need to waggle it around too much.