I have come to this board a couple times in the past asking if my CPU is bottlenecking my graphics, but up to this point I really havent seen a final need to pull the trigger.
E6400 OC'd to 3.2
4 gigs of DDR2 ram
5770 Vid Card
24 inch monitor ( I run at 1900x1080)
Antec True III 550 PS
The story has changed though when I am playing starcraft. I am playing on high settings and once everything is loaded it is fine, but getting there has plenty of stutters in the initial play, and the loading takes a longgg time ( not sure if thats cpu related). I also look at my performance monitor during play and I hit around 96% cpu usage (which once again could be normal).
So I am contemplating doing an upgrade now, or possibly holding out till christmas sales. If I was to pull the trigger I would want a new mobo, lynnfield core, ram and a CPU cooling fan. I want to stay around 400-500 dollars, and saw that an i3 might be a good choice for ocing/cost, and that still around 4 gigs is good ( but up for suggestions).
Its hard to say since you don't have a very high end GPU. If it was a 5800 series, the yes it would.
But lets consider that you do play at a very high res of 1920x1080 (I assume 1920 since I have never seen 1900x1080) that will be more GPU related than anything. It is a possibility that the CPU is holding back the GPU since a 5770 does perform at about the level of a HD4890 which is happier with a decent clocked triple or quad core.
If anything, I would hold off. If your really want a new system a quad would be a better way to go. If you want to go for it now, you could look into a Core 2 Quad since they are still around and would be a easy drop in.