Even with a "non-op"...in CA, you can get a temporary driving permit.....which requires a DMV visit....ugh! Usually only for one day! For moving car "to the shop for repair"...... and back! But I think you'd need to convince the DMV clerk to issue two slips at the same time......??! That could be difficult!!! 
Non-Op in CA allows for avoiding yearly road ransom.... Not sure about personalized plate renewals.... But if you want to remove it, you just send your latest registration paper with check to DMV and wait a few weeks..... No longer a big deal for OLD cars.
For cars/trucks that may be subject to tail pipe inspections, you'd likely need to provide one of them things too if it's been a few years!
I believe that this car was well loved and taken care of! Rubber fuel line would be only item I'd be concerned about aside from old gas and old coolant for the most part. OK, then tires.....
Cheers!
Steve