I can report how my computer handles 4 players in Single player and how it handles 10 players in Single Player.
My Computer is:
Windows XP Professional
AMD Athlon(tm) 64 Processor 3500+, MMX, 3DNow, ~2.2GHz
1024MB RAM
8800GTS
Game Settings:
1024x768
AAx2
Graphics - High
Bloom On
4players Single Player:
Runs great - Even late game with lots of units and AI running amuck my computer seems to handle it pretty well.
10players Single Player:
Runs pretty well - Late game the AI begins to bog down the game and it becomes "choppy" this does not make it unplayable however.
In My Opinion:
Setting the Graphics down and such will not make the game look bad. I have done so on my computer and I think the game looks really good on medium and low. its my opinion that your computer will "handle" the game, you may have to lower your graphic settings but your game play will not be affected in 2-4 player games that much. 6 player and higher, as i have experienced, you will probably see some "chop" late game.
I would get the Demo and check it out if you haven't already. Set up a large game and see how it goes.
Cheers,
Edix