I'm 99% sure the zone valve does stay open during overrun as this is what originally made me question why the external pump wasn't also running. My old system, without the external pump, would have continued to pump water around the cylinder in the morning even when in overrun mode, but the new system wasn't doing that and so the water was only being pumped around the boiler circuit.Might also be worth also checking if it keeps the zone valve opened for the overrun period (otherwise despite what I thought previously) the ext pump will have no pathway for the water, (with/if all zone valves closed), it may not do the ext pump any harm if the overrun is only for a minute or so.
It seemed like the system spent a lot of time in overrun mode, which is what I had assumed was causing it to take so long to heat up the hot water in the mornings. Maybe that wasn't the cause and it was due to my son having secret midnight showers and also having the hot water temp set to 65. It still seems "better" that the external pump should be running during overrun.