Well, at least in part.
The BBC have made rediscovered audio tape of some 16 minutes of William Hartnell's episode of "Desert Island Discs", hosted by the legendary Roy Plomley.
The programme was last broadcast on the BBC Home Service on August 23rd 1965. To listen to this marvellous find just click on the iplayer link.
http://www.bbc.co.uk/programmes/p009y3yj