It depends whether or not your caravan system is operated by microswitches or a pressure switch.
If microswitched, no water will be pumped until a tap is opened to operate the aquaroll pump.
However, if a pressure switch system, then as soon as the pressure in the van pipework drops, the pump will run.
It is wise to switch the pump supply OFF when leaving the van for an extended period.
With a direct mains supply, should there be a problem with the reducer, then water will continue to be fed into the van, which I have seen on several occasions and it is not a pretty sight, and even worse when after time the furniture and cupboards start swelling and falling apart.