I'd be fine with it assuming they cast a suitable actor (which they always do so there's no problem there). You'd have a bunch of jokes in the first episode, many of which would fall flat, but then the show would carry on as normal.
There wouldn't really be much of a difference.
Precisely. For the first episode or two, it would be a gag, and then the show would just go on as it did before. I would only like to add that, if anything, the show could improve as a result of this casting, because they could no longer rely on the whole "hot female companion stares longingly at and falls in love with quirky male hero Doctor" thing I've gotten so sick of.
Oh, and someone up thread, who clearly hasn't examined their own opinions in a while, claims that casting a woman in the lead role would be an "anti-intellectual gimmick." I suppose the all-black Wizard of Oz, The Wiz, was also a gimmick? As was casting Judy Dench as M, and Avery Brooks as the lead on a Star Trek show. All these damned gimmicks - I wish Hollywood would just drop all that politically correct "social responsibility" crap and just get back to the normal day-to-day business of furthering the hegemony of the white male. I mean, jeez. It's just entertainment, for God's sake. (Is there an irony icon?)