Can a 'eC' cooker heat water?
The simple answer is that an 'eC' reconditioned Aga range cooker cannot heat water.
This is a feature not a bug! Using your Aga range cooker to heat water is almost certainly the most expensive way imaginable short of a cauldron over an open fire! Aga range cooker 'back boilers' are simple gravity systems that have no 'off' switch and suck huge amounts of energy/heat from your cooker that the burners , however they are powered, then have to work hard to replace. The simple fact is that these cookers are not primarily designed to heat water.
The water is not heated by an Aga range cooker 'that is already hot' but rather by a cooker that has to work much harder to stay hot! Imagine putting on a coat full of freezing water. Your body will warm it eventually but it'll take a lot of shivering and energy to do it! The pic below shows a boiler from an Aga 'Standard' range cooker, it's exactly like a jacket strapped to the left hand side of the hot barrel.
You are much better off leaving the hot water to your dedicated hot water system and letting your cooker do the cooking.