I don't know about those games too much. I do know:
1. I have it integrated on my laptop. I can play COD2 at high settings but not full with AA
2. I can play COD4 at minimum settings at 640*480 (sometimes 1280*800 on less demanding levels.
3. This is not a card. It is an integrated solution that comes on a motherboard. Its graphics performance is about 1/10th of a radeon 4670 ($70) and about 1/15th of the performance of the radeon 4850($130). the 4850 can acceptably play COD4 at high settings.
The bottom line is NO. you might be able to play those games on very very low settings with framerate drops. Get at least a radeon 4850 for enjoyable performance on warcraft 3.
My old Gateway laptop with a Geforce 6100 GPU and a dual core 1.6GHz turion TL-50 processor can play COD4 at playable framerates on the first level and a couple others. It really hits the chip with the second level with the rain. Considering the x1200 performs similarly, I could see 20 fps being your best not your average. In more demanding levels framerates will drop below playable. My friend has a similar Acer laptop with an x1200. When we play multiplayer with his laptop, we're limited to the "shipping" level because that is the only one where he gets acceptable framerates.
Your second claim with the 2.7GHz dual core does not mention the GPU? x1200? I doubt the cpu would make any difference with an integrated GPU so weak. And honestly, anything below 30 FPS average is unbearable.
So you've heard our arguments I guess. What quality settings do you intend to play warcraft 3?
Also I should have asked before, are you looking at a laptop, motherboard or OEM computer?