Linking an electrochemical cell to an electrolytic cell
For an electrolytic cell, a galvanic cell is nothing else but a power source.
For a galvanic cell, an electrolytic cell is nothing else but a powered electronic circuit.
The galvanic cell anode/cathode does not form with the electrolytic cell cathode/anode a respective separate cell, as there is no ionic flow between them. Similarly for a simpler case, 2 half cells do not form a cell if there is no ionic connection between them.
The reason for it is simple, based on the electrostatic neutrality requirement and enormous forces between unbalanced charges. Imagine you managed to push the current 1 A for 20 s through the wire, without being balanced by ionic motion. The comparable unbalanced charge causes in atmosphere a lightning several kilometres long.