Any monopole antenna such as the ATAS-120 is designed with the assumption that it will be mounted on a ground plane. The geometry of the ground plane is important. At radio frequencies, a sheet of metal such as the roof of a metal car is reflective, just like a mirror. Because the ground plane is reflective, an image antenna is formed below the monopole, making it look like a dipole.
"Monopole and image antenna" by Chetvorno - Own work. Licensed under CC0 via Wikimedia Commons.
If the antenna is mounted on anything other than a plane, then there is no "mirror", so you have no image antenna. Consequently, you no longer have a monopole antenna.
If you don't have a conductive plane available, an alternate solution is to forget the monopole and just make a dipole. This could be two ATAS-120 antennas, each making half of the dipole. If you could figure out some way to mount such an arrangement, it would behave similarly to one ATAS-120 on a ground plane, except it would have twice the feedpoint impedance.
Of course it would also be twice as big, and you'd somehow have to interface to two autotuners. So for practical reasons, this might not be the best approach.
If you take your proposed approach of running a ground lead to the base of the antenna, that might work, but it's important to understand what you are doing. You are essentially making a dipole, with one half being the ATAS-120, and the other half being that ground lead plus the car body at the end of it.
The issue here is that we don't know much about the geometry of this ground lead or the car frame. In theory, you just have a funny shaped dipole, and there's no reason it couldn't be an antenna. But in practice, there are many difficult to answer questions. What will the resulting feedpoint impedance be? Will the autotuner still be able to function effectively? The easiest way to answer this question is to try it and see.
Another approach, if you don't have a conductive roof, is to make one. You can install radials on your roof just as radials are installed in the ground for HF verticals. Run the radials to the edge of the roof, and install as many as you can, I'd say at least 16. The result will look, electrically, very much like the antenna was mounted on a metal body car.