Never really sure how my input will be taken, but here goes. From the Polk's MV Reg Man Volume II which covers all states. Note the entry A, "Special Titles" and "Prior Junk/Salvage" pp.1 and State Assigned VINs" pp.2
My take on this text and the rest of the umpteen pages I skimmed, is that yes you can register a vehicle deemed "Salvage," and it will require an inspection, record search, receipts and possibly an independent appraisal, and fees of some level, but it will always have the tag "Salvage" on the title for the rest of its days. Note on one such adventure they gave me some grief for not enough docs, receipts, for "fixing" the car. On following like events I had receipts in hand which satisfied them more. Some cases they require a "Bonded Title," which can be quite a costly tie-up of funds for three years in my state.
That said, back in the day I knew I guy whose aunt worked at a title transfer business and it seemed he was able to get anything through all the time.
In Wash State, one of number of highly regulated states not unlike Cal, for inspections the State Patrol's, method was, and I assume still is the same, to take possession of your vehicle and sequester it into a garage, close the door and make you wait outside while they do their evaluation. One of my two experiences with state inspections took over an hour and resulted in the Wa State Patrol issuing a new VIN for the vehicle. I was not too thrilled, as they chissled off my original VIN and somewhat crudely attached their universal VIN tag, but there was no recourse and my original VIN was destroyed.
The other time, they left the original VIN and I was more pleased. Both events resulted in title and license qualification. The good time it was near lunch when I arrived, and I sometimes wonder if they were just in a hurry to go to lunch and didn't want to spend too much time on it.
The Polk Manuals I have are bit dated, 1989, but I found them quite useful when I was younger, more ambitious and I bought more cars from out of state somewhat regularly. ...............