I have the same comp and it will run, but be warry of very low graphics. if you're running the older total war games you'll be fine but the new one even chugs on my rig sometimes, so be warned.
How high is the clock speed on the procs?
the Rome and MTW2, you could have 50 cores, and there would be a cap on performance. I have a i7 email@example.com and ATI 5850 6 gigs of ram, and Rome will still get noticeable frame drop with on large units if you are clashing more than 2 full stack armies. For some reason MTW2 is a little better than rome in performance, Rome really wants a processor with an unreal clock speed. i.e. if you had a 2.0ghz dual core you would probably get better performance out of a 2.8ghz single core.
Whereas Empire, never even a hiccup with like 4k soldiers visible.