Do all airplanes have the same turning radius when operating under the same conditions regardless of size and weight?
Take the no-wind case for simplicity.  For a given bank angle, and a given groundspeed (airspeed), there is only one turn rate that will center the slip-skid ball, so the answer to the question must be "yes", assuming that "coordination" is being defined in relation to the slip-skid ball and not some other instrument such as a yaw string.

Due to various interesting aerodynamic effects that happen when an aircraft's size is significantly large in relation to the turn radius, flying with the slip-skid ball completely centered will not always be completely optimum.  Similarly, the answer to the question would be different if the question were to specify that "coordination" were to be measured in reference to a yaw string or other similar instrument located at some given point on the aircraft, rather than a slip-skid ball. For more, read "Circling the Holighaus Way" by Richard Johnson.