Does the positive pole of an an electrolytic capacitor act as a cathode when discharging?
An electrolytic capacitor forms the dielectric by electrolytic action, but mostly it is not an electrochemical cell, once the dielectric is formed there is no electrolytic current flowing in the device.

In Chemistry the the anode is the terminal on the device which an external conventional current is flowing into. In electronics the term is used differently, eg: it's the terminal on a diode which accepts current most readily, a term used to identify one on the terminals of the device, not a term describing an internal or external process.