No, that's the wrong term. Actually, "charismatic" is a description of the worship style, denoting those groups who practice the spiritual "gifts" (greek: charismata) and principally the ecstatic ones, of prophecy and tongues.
There are charismatic congregations with authority structures like you describe, and there are charismatics in more mainline denominational authority structures.
Whatever the original meaning might have been, it has morphed into a belief that authoritarian leaders and strict regimentation are the way to God.