Will motors cause more noise when connected to a ground plane instead of directly to batteries?
There is little choice about this. Quite simply, the power wires to the motor connect directly to the motor and the supply wires to the arduino tee off from the battery and do not go via the motor: -



The reasoning you have given is correct too. Noise can still be a problem to a ground plane so why inflict this unnecessary burden on the power plane of the Arduino or any other MCU that might be controlling a motor.

If it were a dc motor with the control transistor (say NPN grounding transistor) on an MCU board, the rest of the electronics on the MCU board would tee-off their ground from the emitter of the transistor i.e. no motor current through any unnecessary circuitry/ground-plane.