In my experience, mic bleed can certainly add depth and cohesion,
so long as you know what you're doing with it; Cheap mics can sound
really cheap in their reproduction of off axis sounds, so this is definitely something to look out for.
You also have to spend some time and thought planning the layout of the room, and often move things around so that, not only are the spot mics picking up a great tone, but the spill sounds as good as possible too.
And as has been mentioned, any processing you plan to do during post will certainly have an impact on the result - if you want to to severely compress the vocal and use drastic EQ on it, then that will usually have a negative impact on the mix. This is because the vocal is usually the most prominent element, therefore that leakage (which you've made sound a whole lot worse through compression and EQ) will be much more audible.
I really think it comes down to the style of music you're recording - if you're tracking a really great acoustic band, then 'embracing' the leakage will be a much better idea than if it were a rock band. Obviously you're going to do heavy processing on a rock mix, and you'll find you'll be very limited in what you can do if you haven't planned ahead.
If you want to hear an example of how a really good engineer can use leakage to his advantage, have a listen to pretty much anything recorded by Al Schmitt. That guy is hardcore - he only uses mics in omni, no EQ whatsoever, and his mixes sound so lush and have so much depth, it's ridiculous. If you have access to a good 5.1 system, have a listen to the work he did with Diana Krall in surround - it will change your life.
But I certainly wouldn't go out and start recording all my dates here like that - the reason Al gets such a good sound recording in this way is he always records in the nicest sounding rooms available, and he's not compressing or EQ'ing. And to get away with that, well...you kind of have to be Al Schmitt
So in short, yes, leakage can certainly add depth and cohesion, but watch out for phase problems, do lots of experimenting, think things through, and choose the projects you try this on wisely. Have fun!