Will the Intel i3-3220 3.3ghz coupled with an AMD radeon HD 6850 be able to run WoW on ultra with acceptable FPS in 10man raids?
Yes. You might not get a full 60 FPS but, it's more than capable of running it at 50+
I run it on high at 60 FPS with a ATI Mobility Radeon 5730 and an I7 M-620 at 2.6ghz at a solid 60 FPS, I just don't care about the looks enough to bump to higher graphic settings.
I3 might be what's bottle necking you here, two cores isn't amazing but if it's only 10 man, you should be good.
Pop goes the Leman Russ and other fun Lascannon games.
i just did a google search and it looks like they are around 150$ still, and i know microcenter is selling gtx 570s for 150$ if you are lucky enough to live by one, but either way deals on last generations cards are all over, but to your original question that setup will handle 10m at ultra nicely, maybe shadows turned down a notch.
Gigabyte N560OC 1gb gpu
Antec v2 Two Hundred
Razer Blackwidow Ultimate
The keyword you have given us is 10man, which should be ok, but don't expect to be running on full ultra, unless you're playing on really low monitor resolutions.