The guidelines are a little warped on this subject - I deal specifically with total loss and theft vehicles (insurance claims).
Basically, until you;ve had the VIC done, the DVLA won;t issue any documents for the vehicle (V5, tax reminders), BUT, you can still tax the car using your existing V5 - I know that's not what it says on the official website, but equally, Category A and B vehicles are never meant to re-appear on the road, but a recent run-in I;ve had with VOSA has led me to discover that they don't care anymore, so long as the identity hasn't been tampered with.
So in other words, so long as you have a V5, you can do what you like - hoorah for government legislation making the roads a more dangerous place.
The VIC marker is automatically put on your vehicle's records with the DVLA once your insurance company enter the vehicle on MIAFTR (Motor Insurance Anti-Fraud and Theft Register). All total loss and stolen vehicles should be automatically entered on this register, which in turn alerts VOSA, who then in turn alert the DVLA. This will affect all vehicles categorised as A, B, and C salvage - Cat D's do not need the VIC check.
However, having dealt with a mate of mine who repairs scrapped vehicles, this system is not always in place - I regularly check to see if the car is recorded on MIAFTR, and somethimes they don;t have VIC markers against them even after they've been put on MIAFTR.
Is everyone confused yet? Essentially, don't believe everything they put on government websites : )