Is it necessary for the bone to “pop” for an adjustment to occur?

No.  From a neurological perspective, a well-received specific stimulus, however small, can be enough to update, or “reboot” the muscles, glands or any other target of the nervous system. The body has a strong drive to be in balance and in harmony with the environment. When overwhelming or unprepared shock, trauma or stress causes maladapted responses in the body, a simple “reminder” is sometimes all it takes to restores function. Excluding severe tissue damage from violent injury, whether or not our body goes “out” often has more to do with how our nervous system is interpreting the data coming in than the actual physical trauma itself.