So I was wondering whether anyone who has any technical knowledge could tell me how this computer would react to SC2, and on what level the graphics could be set at while maintaining good performance. Also, $1200 is my maximum budget.

http://cgi.ebay.com/Dell-Studio-XPS-1645-i7-2-8Ghz-QUAD-CORE-Window-7-Pro-/330465533192?pt=Laptops_Nov05&hash=item4cf147dd08

When gaming with a laptop, the rule of thumb is usually to never have your graphics higher then medium.
Generally I also do not like refurbished laptops.

Consider this instead:
http://www.amazon.com/gp/product/B00361G0ZO/

This would run SCII just fine, and is well under 1200 dollars.

http://www.newegg.com/Product/Product.aspx?Item=N82E16834115796

I don't at all like the one you posted in that link. It's from ebay for one, and it's graphics card is meh thus nullifying how great the CPU is. If you were to get an i7 core I would recommend this: http://www.newegg.com/Product/Product.aspx?Item=N82E16834152211 as it has a graphics card able to compliment the CPU.