The answers are yes and yes. Yes, you will see a bigtime improvement in FPS. And, again, yes your CPU will bottleneck the 5870.
I once had the same CPU OC'd to 3.4Ghz and it bottlenecked my 260 Black Edition. However, I was getting about 30-40 fps playing Crysis on Win XP w/ DX9.
Go for it, you'll get a big-time improvement over your 8800gts, but will not unleash the full power of the card. Before I got the Black Edition 260 GTX I was running an evga 8800gta and got a dramatic improvement.