There will be less give on the right corner when turning left but more give when turning right, just like having a sway bar that has one loose end. When the air space that functions as the spring in the air shock is compressed because of body roll, the effective spring rate goes up quite quickly, not like a leaf spring that has essentially the same rate throughout its travel. That means that you will likely get oversteer to the left and understeer to the right; the back end swings out in a left turn, then hooks up nicely when you're pointing at the ditch and off you go!

It can be quite an unbalanced response over bumps as well, imparting a corkscrew motion to the car.