It would be a good idea to add some more memory if you want to play Call of Duty at a reasonable speed. 128 MB is it's minimum spec. Your video card is well out of date (Direct X6 generation). Adding the card you suggest and doubling (or quadrupling) the memory would make a heck of a difference to your PC's gaming performance.
Mininmum specs. for games are usually irrelevant, aim for the recommended spec.
Well, the 5200 range are budget cards. They do offer DX9 support, though. The equivalent Radeon 9200 range don't support this. It will become increasingly common for games to make use of these shaders, so the FX5200 makes sense as far as that goes. Really though, the higher specified the card, the longer it's usefulness. Look to your wallet!
I currently have a Radeon 9000 64 MB card installed. I intend upgrading to a Radeon 9600 Pro in about four months time, by which time they should (hopefully) be below £100.