Electronic – Distortion in CAN signal

You would think because of the differential nature of CAN and the fact that you are not drawing power from the OBD port, it would all work fine without the common ground reference.

But, you are then at the mercy of your 2 floating grounds. The CAN transcivier will have an upper limit of the common mode voltage it can tolerate. If at some point the disparity between your floating grounds is large enough to exceed that, you can damage your transcievers. This is not something you can control: so yes use a common ground.

Edit 1:

If however you MUST use floating grounds then consider other (more expensive) transeviers with isolated inputs.

I've done this recently, without needing an ODB-II "simulator" device.

Grab yourself an Arduino CANbus shield and the associated DB-9 to ODB-II cable, and hook it into a car. Write up some code to read CAN messages and transmit them out via serial. Dump this data from serial to a file on your computer. You can then invert the process and transmit the CAN messages over serial back to the device, in a loop, to simulate the vehicle idling.

If the device under test just passively listens into CAN messages, you may need two CAN shields: one to loop the transmission, and the other to actively receive the messages on the other end, while your device under test hooks into the CAN lines in the middle. I'm not sure why this is necessary, but it was for me; the transmitting CAN shield would not initialise the transmit buffer unless I had something explicitly "accepting" the messages at the other end.