I have a Chevy Tahoe which means I have to use a GMOS-04 adapter to hook up the AVIC-D3. On the adapter, there is a black wire that can be connected to the ground wire on the radio. My question is, if I'm doing the bypass, can I still hook up this black wire to the ground wire on the radio, or should I just connect it somewhere on the chassis?

Either should be fine. A ground's a ground, when you get down to it. I personally would ground everything, including the radio, to a chassis ground. I don't trust the integrity of the car's factory radio ground. I've had some bad experiences in the past.