In video, you would not normally adjust shutter speed to control exposure. Changing the shutter changes the amount of motion blur which gives a different "feel" to the video. For 25fps video the standard shutter speed is 1/50s. You can set it slower (to exagerate MB) or faster (for when you want to slomo the shot, or for special crispy-looking effect on the video) but it's not so good if it is changing all the time for no reason.
For DOF control, of course you can close the aperture to widen the DOF, provided you have enough light. Outdoors should be no issue, but indoors where there is less light, and where you are unable to add lights, you either need to open the iris or increase the gain (ISO). Given the choice, I expect most people would open the iris rather than increase ISO, and when the lens is wide open or close to it, that's where you would have to cope with the thin DOF from the 5D2.
But I wouldn't count the thin DOF on the 5D2 as a point against it. If the DOF is too shallow, you can close the iris and compensate with ISO, which will give similar results as the 7D under the same conditions. And when you really want the thin DOF, it is available on the 5D2 but not on the 7D.
Anyway, as I mentioned before, I think the 7D is better overall for video because of the selectable frame rates. Compared with conventional videocams, both the 5D2 and 7D have phenomenal DOF range available and if I was planning to buy one of them for video shooting, this would not be a major factor in my decision.