It should be fine.

If you try the demo, also be aware that it's a very, very old build and Ironclad has done some quite noticeable lower-end performance optimizations since then, so if you're content with how the demo runs the full version has quite a good chance of running a bit better as well.

Well that's good news.

What I'm wondering is my graphics card going to make a difference in that graphics?

I've played this game at my friends house and he has a... GeForce 7800 or something maybe 8000 something, but he has a faster processor.

Will my game run better with the better graphics card, or is that more dependant on overall processor or performance?

Sins cares more about memory and processing power than your graphics card. Obviously if you crank up AA and bloom and try to zoom in on several hundred ships you'd need a decent card, but it's still heavier on AI and calculations - every ship you build has its own AI, in addition to the overall player AIs you may be playing with, so on the bigger maps with lots of planets and all 10 players your memory and CPU are going to get butchered first