No, for many reasons, but here are the main ones: a) Many episodes from the 60s are missing, due to the BBC's wipings of many TV episodes from that period, so thus the idea of a complete collection is impossible to begin with. b) It takes a long time for episodes to be restored and in some cases the Restoration Team have to wait for new techniques to be available to them before they could even consider giving a particular story new restoration. c) Not all the stories have been released on DVD yet, they've nearly finished, but it's taken more than a decade, which shows just how much effort is put into each release.
Above all else would you really want a complete collection of Doctor Who? It would such a huge box set that it would cost at least £600 and no one wants to pay that much up front. We're talking about almost 250 stories amounting to nearly 800 episodes, so you'd be getting so much all at once you wouldn't know where to start.
So I wouldn't be expecting a complete set anytime soon, if ever. Star Trek hasn't done it with their 5 shows and 11 films,so it's incredibly unlikely Doctor Who will, especially when Trek is handled by a major Hollywood studio.
I've nearly got the complete classic stories on dvd, jst waiting for The Tenth Planet, The Ice Warriors and Terror of the Zygons to come out of which they are all on pre-order - I'd only sell them for £100,000. Any offers? lol