What a steering damper does is it deduces the possibility of tank slaps/head shakes but not eliminate it completely from happening. Usually in most cases, hitting a pothole or a ripple won't cause head shakes if your gradually accelerating or holding your current speed. It usually occurs when the front forks are extended and the bike is accelerating hard, most of the weight is on the back and front is very light.
Under hard acceleration, hitting a ripple will cause the forks to compress, slightly off centering the front wheel. Then, your forks unload, decompress, centering the wheel, but not completely straight. Then, while the wheel is slightly off centered, the forks compress once again hitting a ripple/pothole imperfection on the road. This process repeats itself causing the handle bars to shake, front end, your arms, your head, your shoulders, and if you attempt to correct it by excerting your upper body strength, tightening your forearms, hands, shoulders, the wobbly travels through the rider and the whole bike becomes unstable.
If such stiffness can cause the whole bike to become unstable, is it possible that if the steering damper is on too tight or on the wrong place, it can have the same effect. Yes it can. I'm not a big fan of steering dampers mounted at the top of the steering head attached to the top of the frame. They work best, when its mounted at the mid-section of the forks and when they are not on too tight.
From my experience, I never had tank slaps or head shakes just cruising around at lesiure. It happened to me twice when, throttle was pinned, and my most recent crash, off roading on my Gixx.