I don't know what antenna you are using. I'm using a FT-897 with an ATAS-120a. It would not tune, until I grounded it properly. Also, I was a bit curious about how the lack of a metal roof effects the ground plane.
In any event, the documentation on the antenna, and everything I have read suggests strongly in properly grounding the radio and antenna. One nice thing I noticed the way I wired it all up, there is absolutely no feedback from electronics, engine noise or anything. I had read that a couple of folks had issues, with radios tripping various sensors, though I haven't done much transmitting at this stage.
The radio will pick up noise from a **** eater running a block away, but no engine noise, so that's a good thing.
An example, on having read quite a bit about properly setting up the rig.
http://www.diamondantenna.net/Product_Catalog/HFmobiletips.html
I ran a strap from the antenna base, folded and tucked under the roof rail, tacked with silicon seal to hold it in place. Then ran it under the plastic end cap, toward the rear of the vehicle. Then I put another corner fold on it, and ran it to the left grounding strap under the rear upper door. (There are two grounding straps running to the rear door, one on the left and one on the right.
What Antenna are you running?
Boy it is the perfect solution though... I have found nothing else like it.
