Depending on your resolution, no I don't think that it will. The onboard 3000 is really... bad and old as well. The CPU will be plenty but its not exactly good on graphics.
I suggest learning to build your on PC. Go to Newegg or Amazon and pick parts.
For a guide, check the one in my siggy out. That will help alot for a beginning builder. That 600$ build I have would be well worth the time to learn to build, It'd also give you pretty future proofing tech.
No, no, hell no lol. The ATI Radeon 3000 integrated graphics benchmarks even worse than an integrated Intel HD graphics.
I'll assume $599.99 is your budget. I don't know where you live either, but lets assume for a minute its Oklahoma. www.bestbuy.com, the seven digit numbers are the SKU's (I tried linking them but it wasn't working)
Take this computer: 1677193. $419.99
Video card: 8968094 $99.99
Power Supply (The one stock won't cut it): 9827301 $64.99 OR 9827268 $89.99 ($89.99 better for more watts in case you do future upgrades)
Done! It'll run better than medium settings! Your probably wondering if the processor will be enough: definitely will be. The video card will be more important than a quad core processor. In fact, Starcraft 2 only supports up to 3 cores anyway. In fact, ultra high settings on most categories! Now I assumed Best Buy because its possible you may want them to install the power supply for you, as I'm not sure if you felt comfortable doing that on your own. I believe its $49.99 or less in labor to do that. Do yourself a favor though and save money and don't pay $29.99 for them to put in the graphics card. Its pretty straightforward to install that. But if you want, have them do that too.
Bottom line, its better to do this in terms of cost, even when you account for labor. Your paying a little more than $599.99, but the result is a better computer then you'll ever get stocked. If you have the money also, pick this desktop instead and do all that: 1677209
Doing this doesn't void warranty either since Geek Squad will install it for you. Also, you can order this stuff online if your store doesn't have it, and as long as everything remains sealed, you can bring it in and they can install for you still. Now I realize Best Buy gets a bad rep on Toms Hardware, but in reality Geek Squad does these installations all the time. The rest of the stuff they will most likely pitch to you sales wise is up to you (aka 4 year warranty with them, etc.). Patience though, they also get a bad rep for trying to sell you a lot, but its mainly because for reliability reasons so customers don't come back pulling the "they didnt' tell me this" card.