Generally speaking as long as you stay above 30 FPS you will get a fairly smooth experience. Once you get below 30 FPS things start to get choppy. 60 FPS is ideal, but anything 30 and above is certainly playable.
In very laggy situations you will barely reach 30fps (I mean really really laggy), And in normal situations it will have 40-50fps. Sometimes it would even reach more than 65fps but that I think this is the Maximum. It is really playable.
I have an 6950 2gb video card, I play BF3 with automatic setings , and with automatic sime settings are on ultra and some on high. I play on a 1920x1080 with max resolution and here are my results registered with fraps :
Frames, Time (ms), Min, Max, Avg
1163, 17036, 51, 94, 68.267
My card is not moded in 6970.
You will only get choppy gameplay if your FPS drops real low, even at 30 the game can play smoothly. The 6970 is a great card, but if you are really concerned about performance and you want something more , save up some cash and get 2 x 6950 and crossfire them if your mobo and psu support it or get a 6970 now and crossfire with another later.
With AA and MSAA off it will give you even smoother game play as you have reduced the strain on the card.
Give it go , BF3 is a great game and is a lot of fun , you wont be dissapointed using a 6970.
Crossfiring later will push your performance even further.
Yes it does , best thing to do is to play around with the AA and AO settings and see where you are happy with both the quality of the image and the performance. I don't see you having any problems at all with your set up.
I play BF3 on my ancient radeon hd 4830 and have more fun than any shooter I've played in a long time. All settings on low (LOL) and it still blows me away how good looking this game is. Frames Per Minute is probably a better unit of measurement on my PC though, haha.