For sure,
I only have a AMD Sempron 3000+ 64BIT, ATI Radeon 9600 Pro Advantage 256MB, 512MB DDR400, 30GB Hard Drive (Slow like c...) and BF2 works at medium quality with 1024x768 resolution.
No you wont.
I have a AMD 64 3000+, 512mb, agp x800xl 256mb.
I can run at medium but get some lag/jitters every two minutes. Upgrading the ram should sort this out though as BF2 is very RAM dependant. Upgrade to 1.5gb and yes medium/high should be achievable.