Yes, and Kevin Cameron mentions in his Sportbike Tuning book on p103 in my edition how there are two instabilities. They are wobble and weave. Wobble is the fast type of 8-10 seconds, what is most oven considered handlebar shake, usually when accelerating or decelerating around 35-45 mph. The other is weave and is about 2-3 cycles per second. A steering damper can (read:might) make weave worse. Ideally, if instability of the handlebars is never an issue, then you don't need one.
Also, weave is more likely the higher the speed. I think that may have been what happened to me a couple weeks ago, that I posted about to ask others their experience. And supposedly, every bike is prone to weave if the speed goes high enough.