You can clay pretty much anything you want to on the car; wheels, glass, plastic trim (great way to remove overspray from crappy paint jobs); basically you name it. That's why I like claybars so much; they're really quite versatile, and foolproof. As long as you keep the surface lubed, let the clay glide over the paint (or glass, or whatever), check the bar for debris regularly, and wipe down each area with a nice microfiber towel when you're done, you pretty much can't do any harm to your finish.
The clay won't damage the emblems at all; just be sure you keep enough lube on them, so they don't get streaky-looking from the clay residue (even if they do get that way, a quick wash would clear it up). Actually, that's one benefit of debadging the car; it gets rid of the odd nooks and crannies near the badges, so waxing, claying, and polishing become easier. (Plus the lines of the car flow a lot better IMO)
I'm not sure about the stickers; I haven't tried claying over decals before. I imagine they'd be fine though; I'm sure the adhesive that holds them on there is pretty strong stuff, and as long as you aren't forcing the clay bar against the surface, you shouldn't mar or tear the decals themselves; I bet the acrylic or whatever they're made of is pretty durable as well.
Not sure if I mentioned it in here or not, but claying can remove wax from the paint, so if you had a coat of wax on the car, it'd probably be a good idea to re-wax it after you're done claying.
One minor disclaimer: I'm assuming you're using a claybar bought at Autozone/Walmart/etc., as opposed to one bought online. The only reason is that some of the bars you find on detailing supply sites are what's known as a "medium grade" clay (they're all clearly listed as such, so you'd know if you bought one); that means the abrasives in the clay are larger. These are some pretty heavy-duty products; in fact, I'd try to avoid using them; I've seen some pretty badly swirled finishes that were the result of medium-grade clay not being followed up by a finishing polish to remove the swirls. In my opinion, if a normal (fine-grade) claybar won't fix your problem, it's time to polish the car. I'm almost certain it doesn't apply to you, but it's another little tidbit of info that could avoid some problems in the future.