We had a 172R that some lowlife took an axe too, it was written off and I marked all the logbooks up accordingly, I do not think there was a single skin left intact and the prop had been done as well, so I wrote in both the Logbooks that it was written off and it had suffered a prop strike too so needed overhauling..... it had been cancelled of the register as withdrawn from use as it was written off. The hull was bought and rebuilt by another company in the UK and reregistered ( a sensible idea as we did not know the motive and if a grudge was held over this one aircraft a change of reg is a good idea )
As long as all parts are replaced or repaired in accordance with the book then i cannot see a problem, one issue that will never leave it though is its damage history and like a car that can have a significant effect on its post rebuild value. You will be pushed to sell it with no prior history before the rebuild, people will want to see or have the logbooks etc and I would have thought you would need to legally state its history otherwise it might come back to haunt you.
I believe the previous logbooks must be retained for 5 years? or 2 years after an aircraft is destroyed, so should be available and I would imagine before it is reregistered your CAA would wish to inspect it and the paperwork