I thought about running a separate large gauge ground wire back to the battery when I put it in. But I didn't, just lazy, as I recall. I may not have thought of it until after I had already run the power wire, and put the carpet and seats back in place ..
Grounds are definitely important. Our ECM, TCM, etc. controller specifications usually specify the controller must function normally with up to a 0.5V ground offset from the battery, although that number has bounced around over the years. I've never worked in the audio area, so I don't know if the radio head has a more restrictive requirement.