No, your framerate is not dictated wholly by your video card. Never was, never is, never will be. (unless future computers are nothing but video cards)
Rather, your framerate is determined by whatever the slowest thing is in the whole process of running. In an MMO, that usually tends to be the connection and server; the computer has to sit there waiting for the data, and has to be ready to drop everything when a packet arrives. If it's inefficient enough, yes, the CPU will be slowed down and stuttered as it places priority on sending and receiving data, cutting off how quickly it can assemble frame data to send to the graphics card.
And if the graphics card can't get the data it needs to draw each frame quickly enough, not even all the graphics power in the world can allow it to get 60fps; it's a domino effect.
This is actually compounded by the use of vertical sync; for that, the game will only ever flip a frame if the time evenly divides into 1/60th of a second; if the CPU was late in getting the data to the graphics card for the frame at 05:07, (seconds:60th seconds) the graphics card will wait until 5:08 before it "flips" (displays) the next frame, whatever it is... So If the CPU gets the data out at 05:07.01, and you've got a graphics card that powerful, then it'll probably finish the frame before 05:07.10, and then spend the remaining 90% of that frame's time doing nothing. As a result, you get a strong domino effect where a tangle at one point in the line holds up everything.
I mean, seriously, the 4850 is stupidly powerful for World of Warcraft; that's a game that was designed to run fine at medium resolutions on ancient hardware like the GeForce 6600GT. Something like the Radeon HD 2600XT or GeForce 8600GT should actually be sufficient to get 60fps even at your high resolution.
If your reduced framerate is causing stutter that you can see, my recommendation is to actually disable Vertical Sync. That way the graphics card wouldn't bother waiting and will go ahead and flip each frame as soon as it's finished drawing it. The game will still have stutters, but they will no longer be rounded up in length to the nearest 60th of a second. The downside of disabling this is that your framerate will shift more than normal, but with the CPU being held up like that, I doubt that it'll actually be noticeable or even really show up.