Whilst technically you may be able to play BC2 with the 4350 I suspect your frame rate will be quite low. A Q6600 and 4850 gives me an average of 30-40 fps at 1920x1080 across the settings on the beta. I think there is still optimisation to be done for the final release as the differences I see across low-high settings and resolutions are not necessarily what I would have expected (often seems like almost no difference), but BC2 seems to be quite demanding on hardware.
This is why I wish everyone would put demos out for a release. Yeah demos run a little rougher but you can play it to see how you like the game AND see if it runs ok on your system. It is hard to mix and match minimum hardware requirements. If you have a quad core and 6GB of RAM, then that is a leg up from the dual core and 2GB RAM so can you eek out decent FPS with a 4350? Probably but by how much...who knows.
I would bet that after the release, they open the beta up as an official demo. They have done so for BF2 and BF2142 and EA is trying to compete like crazy against COD.
Duster, you could try to register for a Beta key on the EA site. Maybe you can get access and try it out.