Pretty sure it doesn't. I can't say for sure, but darker juices almost always clog cartos and destroy atties quicker. Theres a reason for that. Someone correct me if I'm wrong, but it seems like the darker juices have a lot more particulate matter in them, most of which won't vaporize, so you still more or less get the flavor from it but at the same time most of it just burns onto the coil, or potentially stays in the wicking/filler. I could be completely wrong, but since most darker juice does have a tendency to stick in an atty longer and shorten carto life, it'd make sense.
Now that I think about it, two more reasons why I doubt dark e-juice stains your teeth.
One: The condensation in a drip tip is normally clear, even from dark juices. Either A. The heavier, darker particulates don't condensate that easily or B. They just aren't really in the vapor at all, previous point.
Two: Smokers get stains due to tar and such. Tar is NOT water soluble, as far as I know. Even with oil-based flavors, PGA has to be used to MAKE them water soluble, so even if the vapor could stain your teeth, I'd think it would wash off fairly easily. Some may say that coffee is, of course, water soluble, and still stains teeth, but if you think about it, thats a very dark liquid completely immersing your teeth whenever you happen to drink it.
When I first started vaping, I did something kinda silly. I filled a little plastic souffle cup with cotton balls, poked two holes in it, and blew vapor through it every hour or so for a few days. I lost interesting as nothing really happened, but that, I suppose, kind-of proves my point in a 2nd grade science fair kind of way.