BF3 is gpu intensive and can be run on a dual core cpu so the answer to your question is that your cpu will not or should not be much of a problem and you will see the maximum benifit of the card , I do think that if you put a high end card or multiple cards then you would start to see some bottleneck.
My last set-up was a Core 2 Duo E6850 running at 3.7ghz, paired with a GTX 260. Using MSi Afterburner to monitor GPU usage, most of the time my GFX card was sitting around 45-85% usage while my CPU was maxed at 100%, and i was getting pretty bad performance. Once i upgraded to a i5-2500k, that bottleneck was removed and now my GFX card is running pegged at 98-99% all the time in games.
So to answer your question i was running a similar, slightly better CPU and was experiencing a terrible bottleneck even with a GTX 260 which isn't even that fast of a card anymore. The GTX 560 ti would not reach its full potential with the E6600, but would annihilate the 8800GTS no matter what. I also had DDR2 ram in my original build and when i upgraded to 4gb of DDR3 and a new motherboard i noticed a nice increase in speed also.
If you have the money i would suggest thinking about a new computer build IMO, but if you do not, the 560 ti would be a very noticeable increase over the 8800GTS while you save up for a new build and would still be a good card by the time you have the money, very much unlike the 8800GTS, which is already far past its prime. So in short, build a new computer if you can, and if you cannot, buy the 560 ti and save up for a new build.