Nah, if they had been hired, the tardis would have changed it's exterior to look like K-9 and they would hop out of his poop shoot to exit. There would be no Gallifrey, but rather the doctor would be from the future of man and part of a large time directorate stationed on Mars (where the doctor would have been born incidentally). The K-9 tardis would be armed with Photono Torpedoes and Phasic Cannons (the torpedoes would fortunately have an explanation for never running out in that the tardis has limitless storage space... or would it anymore?) The Daleks would now have ridges on their domes, and be honorabe beings that would form an alliance with the Doctor as he tried to find out who the real villain was that was causing all the trouble throughout time. Oh, and the doctor would no longer "regenerate" when he dies. It would turn out that the Doctor is a shape shifter (great for all those cool stories they would want to tell) and he was never really dead, but rather faking it and changed shape to a new form for convenience. Yeah, that's it.
btw, I'm gettin' kinda bummed about this doctor leaving. I think he might be my favorite since Baker, at least thus far. I am really liking the series, it seems to have a lot of the flavor of the old but updated. I'm shocked that someone is actually pulling off bringing back a series without totally raping what has been done before. I don't believe it's been done before, at least not in recent history, imo.
As far as what happened to the timelords, beats me. I guess the above explanation is probably the case, but I thought he said they were all dead, not just moved out of the house, and the planet destroyed. Guess I'll have to pay closer attention. I figured it was something that happened between the old series and this one, especially given that they didn't open the show with an old doctor changing into a new one (which they did with the FOX TV movie) so who really knows what's happened between then and now. He hasn't said which incarnation of the doctor he is, for all we know he could be number 11 or 12, I'm guessing it's not (they only have 13 lives, right? Been a while since I heard about it) but really any amount of time could have happened between then and now. I wonder if they are leaving room for some of the books and other adventures that contained to the FOX doctor (can't rememeber his name at the moment) to have taken place without actually going through producing them. I haven't read any, but I saw some pics of book covers and whatnot, and there were some audio adventures and online little animated adventures featuring him if I recall. I guess we'll have to see. I'm really enjoying have the doctor back though.