BFV's pretty fun, I recommend it.
Computer-wise, yes, you can turn down the eye candy and run it on a number of machines. The video card does 80% of the work, but the CPU has to be fast enough to pass triangles to the video card. If you have a nice video card and an ok CPU, then it looks really good!
BFV will run fine on a 64MB or 128MB video card. It doesn't use all of the 128MB video card, so a 256MB video card will not make a difference. The # of MB does not determine the speed of the video card. You'll be much better served getting a 128MB 9600 Pro than a 256MB 9200. A 256MB video card will be useful next year...so unless you're getting a 6800GT, the 256MB won't be of too much importance.
I'd say the best bang for the graphics dollar is at a minimum the 9600 Pro 128MB (~$100). Moving up to the $200 9800 Pro (must be 256-bit!...but 128MB is fine) will really blow your socks off. If you can wait a month, then I'd go for the AGP version of the 6600GT ($200) and looking to perform above the 9800 Pro. The CPU should be somewhere above the 2GHz mark (or above 2000 mark for AMD's...1800...fine).
The GF440MX, RADEON 9200, GF5200 and others in that class do have 3D acceleration, but are woefully underpowered. I know...I've got each of them in different computers that do different non-gaming duties. The higher end cards really make a huge difference!
I've got a little AMD box here...I had a GF440MX in it at first...besides, I don't play many games on that machine. I run 3dMark03 on it for fun...then I upgrade the CPU only and do it again..then I upgrade the video card only and do it yet again...
Duron 1.6/GF440MX...3dmark03=206
AMD2700XP/GF440MX...3dmark03=226 (graphics card does most of the work)
AMD2700XP/ATI 9600XT...3dmark03=3733!
Here's Tom's Hardware on the subject using BF1942 (similar engine, not as much eye candy). Their test is with much of the eye candy turned off.
http://graphics.tomshardware.com/graphic/20031229/vga-charts-04.html