ljcox,
No charge flow, no current.
Apparent current is an equivalent current, a current that would exist if the magnetic flux inside the capacitor were produced by a current instead of a changing electric field intensity. It is analogous to the mechanical equivalent of heat. A bowling ball rolling down an alley has kinetic energy (KE). That energy can be expressed in heat energy instead of KE. The moving bowling ball represents virtual heat, even though its temperature has not risen. The apparent heat energy is not really heat, just an equivalent KE. The apparent current represents the equivalent magnetic flux density (B-field), even though the apparent current did not product the B-field. The changing electric field intensity did.
Ratch