Is an ATI Radeon 4250 HD graphics card sufficient enough to run SC2?`

Uhm no its NOT slightly better it is, it is by far worse. At best its (and this is a huge stretch) the 4250 is 40% of the 3850. the way the model numbers work is the 1st digit (4, 3) indicates the chip-set series or family (the 4250 is a new card). The next digit indicates the target market/level 200s is the lowest end of the spectrum usually for integrated chips (lowest entry level); the 800s are for enthusiast (one step below top of the line hardcore) the 3rd digit (5, 5) is the level for that card 30s are for nerfed versions of a card, 50s are the standard card and 70s are reserved for the suped up version of that card.

Here is a wiki link to see the whole family of radeon cards to get a feel for things

en.wikipedia.org/wiki/Comparison_of_AMD_graphics_processing_units

I actually have a HD 4250 this is comparable to about 2x the speed of the the minimum specs for SC2 (radeon 9800, a card from 2003). You will be able to run the game on low settings smoothly assuming your other specs are up to par. The game is very CPU dependent, it is optimized for a dual for so you need at least that other wise your cpu could bog down everything else. The same hold true for the ram; a special note here min is 1 gig recommended is 2gig. Short this and things will get ugly i recommend 2gig as well to avoid lag from reading the hard disk. Special note many video cards , especially integrated ones tend to use the system RAM in place of VRAM it does not have, check your system under my Control Panel to see what actual RAM is available. In my case the 4250 borrows 512mg leaving me with only 1.5gb for the system (actually short of the recommended) .

If you want to upgrade keep the benchmarks in mind:

www.techspot.com/review/305-starcraft2-performance/page5.html

30fps min is what you want for smooth gameplay. On the cheap i would recommend a GT 240 (Gddr5 version) which you can find for under $50 after rebates, the next step up id recommend a hd 5750 (can be found for close to $100), and for the best possible performance you don't need to get anything over a GTX 460 (can be found as low as 185 for the 768mg version and 210 for the 1gb version). Hope this helps you out. and if you are on SC2 let me know we can meet up for a game.