It's a good question. With a mono mic, there is no "pan" of the sound, as that term refers to the movement between channels in a stereo sound field. In mono, the sound is always centred, so tracking the movement of the car with the mic makes no difference to the spatial effect. However, if your mic has a directional pattern, i.e. is not an omni, the thing that you would gain by tracking is a fuller representation of the Doppler pitch change as the cars go by. At legal urban speeds, this is a small change, but is perceived subjectively. It would be more noticeable on emergency vehicles travelling at higher speeds and using sirens.
What you should be using is a stationary stereo mic set. I occasionally go out and sit lineside to record steam train special workings, and for that I mostly use a spaced pair of small diaphragm condenser mics on stands with omni capsules fitted. Despite the omni capsules, I still need windshields even on a still day because of the air disturbance caused by the train passing. I also take a secondary recording on a Zoom H4N recorder using the X-Y built-in mics, but it's much more difficult to get a satisfactory result with a co-incident pair and a very wide sound field.
The other factor in your case is whether the vehicle is the only sound source in your recordings. If there are other prominent sounds, it makes sense to have the microphones stationary (not tracking the vehicles) to keep the other sounds where they should be.