Echoing skeletron's comment, in practice my choice of where to put the shear plate will generally be governed by spatial / geometric concerns and it often winds up on the shear center side as a result.
The theory is interesting though. With reference to the beam end free body diagram shown below, I believe that it works out like this:
1) From the perspective of torque on the beam, it doesn't matter where you put the plate. The torque that the plate will introduce into the channel will be identical whether the plate is on the shear center side, the non-shear center side, or in the building next door. The channel torque winds up being a function of only the load and the distance between the point of load application and the channel shear center. The channel torque would seem to be agnostic with respect to the location of the shear plate.
2) Putting the shear plate as close as possible to the line of action of the load will reduce the torque on the shear plate though. Not that anybody checks that.