Well it is "possible", but when a shock goes bad, weight reverts to the spring. With only 1 bad shock, the weight difference from side to side could be causing the "bad shock side" to be going from resting on the spring's load, to raising the shock up some. This would cause a noticeable shudder and some immediate over/understeer, but not a constant shake at highway speeds.

Do you spin your tires alot? Did you buy them new? It only takes a small warp in 1 single tire to cause a shake.