Well I didn't start up the motor even though I was under the impression It needed to start. All they did at the CHP was check the VIN , lights, mirrors, signals, tires. Didn't have to start it or even turn it on to show stuff works but who knows what your CHP may want - might as well be prepared. So I think you should be able to drag it down to your CHP for the inspection as is. Call and ask them what they will check. They are nice. You will need an appointment anyway for the inspection as they don't do them every day. Then you take all the paperwork from that inspection to the DMV for the title and registration and plate.
Possibilities are: (1) the VIN is not in the system and you're good to go, (2) VIN is in the system and you will have to come up with a transfer or BOS from the last known registered owner - more complicated, and (3) VIN is in the system as stolen in which case it's best to know now but I don't know what the outcome will be.
Before I bought my frame, I called the CHP and asked them to run the VIN first which they were happy to.