If the boiler and pump starts and stops when you turn the cylinder stat up or down when switched to hot water only, it indicates that the cylinder stat has been rewired to bypass the missing actuator. If, so, it will be OK to leave it as it is, bearing in mind that if left like this you will be getting a gravity flow from the boiler to the cylinder for a while after the boiler and pump has switched off. Also if left as it is, you should close the bypass valve, as the manually opened HW valve acts as the bypass.
In my example, after explaining this to the customer they decided to have it rectified.
In my example, after explaining this to the customer they decided to have it rectified.