I would always provide ground for the RS232 signal to minimize the path inductance and minimize interference (i.e. the minimum RS232 connector would normally have Tx, Rx & Gnd).
However, in your case, a key question will be whether the client-provided PSU and RS232 kit are isolated from each other. If they share a common ground (which your question implies), then potentially a significant fraction of the motor return current could flow in the RS232 "Gnd" wire (whether this is separate or combined). This can cause problems due to shifts in the reference level, especially if the motor current has lots of transients. It may also burn out the wire.
RS232 is pretty tolerant, so you might not have issues, but for industrial environments, my default approach is always to have galvanic isolation on control interfaces to avoid this kind of problem.
It comes from free with Ethernet (which is transformer isolated), and there are off-the-shelf isolator chips for RS232 (including charge pump supplies for Tx) that work very well.
Summary: Do provide a "return"/"gnd" wire for your RS232 interface, but galvanically isolate the RS232 interface from the rest of your circuit to avoid "entertaining" problems in the field.