no..... the radeon HD6450 is a continuation of the HD5450 which is basically designed for media centers and general desktop pc,s used for web browsing.... however the limited 64bit memory interface and slow core and memory clock speeds make this card unsuitable for gaming.Blizzard recommends at least a 5770 to play WOW. You could look at that card or the 6790. If you're on an extreme budget then at least get the 6570.
But although taking into account the above providing you are not running the game on to high a setting or on a to large a monitor then the card/PC will be fine and you could look to upgrade your GPU in the future. Overall a fair PC for the price. I notice that it does not come with an operating system, have you got that covered?