I remember an old interview with RTD from his first run where he said that by now the Doctor has become part of the national folklore like Robin Hood or Sherlock Holmes so it'll never truly go away which I think is true. Even if the TV show goes away again for a while, Big Finish will keep going, people will keep writing books, there'll be fan fiction etc.

And presumably it'll have to enter the Public Domain eventually too, although that's probably still a long way off.