If you are referring to the Phenom X3 8450, yes... your processor should be able to keep up with the demands of the GTX 560. That is, assuming you have a board with at least 4GB DDR2 or better memory, a fairly recent Hyper Transport version, and your gaming isn't done above 1680x1050 resolution. Bottlenecking is highly over-worried. Yes, it occurs, but it isn't a game killer in most cases. It just means your Graphics card will wait a cycle or so for the CPU to process the frames it sends. Remember... good gaming is mainly about the graphics card.
Your minimum FPS depends much on your CPU.In your case it might even become unplayable at some point.
My older system had the same CPU as yours.During heavy firefights fps would dip below 16 in bad compnay 2.Now I have i5 2500 while the gpu remained same the fps never go below 31.
In my opinion you must change the cpu or it will severely bottleneck your gpu.