Well, yes - the question of whether a TV programme called Doctor Who also exists in the Whoniverse obviously gets rather meta-referential! But it is played around with in the Seventh Doctor story, Remembrance of the Daleks (http://en.wikipedia.org/wiki/Remembrance_of_the_Daleks#Continuity), which takes place in 1963 and includes a scene where we hear a television announcer introducing "the new science fiction series Doc--", but getting cut off before the title is completed.

Other than that, though, the show does generally try to maintain consistency with our universe. The point has become sorely stretched in the new series because it focusses so much on present-day Earth, but it was definitely adhered to very strictly in the era I'm writing about here.