You wont only be using 'up to 6 Gb'.
Your total ram use will be higher than that if you also add the amount of cached ram shown in smaller text underneath the graph.
When you look at Vram usage in afterburner, you get your current vram use + cached data in your vram combined together into the vram usage graph. When you look at ram usage under the performance tab, it doesnt add used ram and cached ram together, it displays them seperately.
When you only have 4 Gb system ram, you will have nothing left over for data caching. Combine this with 1 Gb Vram and you are going to constantly see lag spikes and stutter in so many games because you simply have non existent data caching on your system.
This is resolved via either more Vram, or more system ram, and right now 8 Gb system ram is so cheap compared to +1 Gb vram that I really have no idea why people who are still only using 4 Gb ram expect to be able to play anything without lage, especially if they only have 1 gb Vram.
UPGRADE TO 8 GB SYSTEM RAM BEFORE BLAMING VRAM AS THE CAUSE OF YOUR LAG, ITS CHEAPER!
30fps is enough to play smoothly if it never goes any lower and both those results are still not consistent enough.
30
AVERAGE FPS is nowhere near enough to play a competitive online FPS game, you are going to have a lot of lag, and even if you genuinely dont notice it, you are going to be losing a lot because other people with higher FPS have far quicker and smoother accuracy and response than you do. 60 average FPS and 30 minumum is playable for a game like BF3 while playing online, this is a completely different scenario to the graph in the OP showing a 2 Gb GTX 560tis performance as constantly dipping well below this. Those figures in a game like BF3 will be unplayable for everyone.
When I enable video recording at 30 FPS, my games slow down and begin to lag. If I increase that up to 35 FPS, the lag smoothens out, but camera turning / map movement still has a lot of stutter and skipped frames. I only experience fully smooth gameplay if I can maintain a minimum FPS of 35-40, and an average of 50-60.
Having said that, a single card pretty much never provides me with playable framerates in the latest games, regardless of whether it has 1 Gb Vram, or 100 Gb Vram. On the other hand 2 x 1 Gb GTX 560 tis coupled with 12 Gb of very low latency ram has yet to produce any kind of lag or microstutter in any game out there today. BF3 on Ultra graphics settings but at 2x AA would be fine if I maintain a 50+ FPS average, and 35+ FPS minimum. I strongly doubt that a pair of 2 Gb 560tis would manage this at 4x MSAA over my 1 Gb cards at 2x MSAA, so the extra Vram would be entirely pointless if the GPUs cannot push enough FPS for smooth gameplay in the first place.
Also Vram cant be the reason why BF3 lags with 4x MSAA, judging entirely by the same amount of performance loss on 2 Gb AMD cards.