Actually, the thought process is sound in one respect: the turbine engine of helicopters is far more efficient at high power settings such as that required by an OEI situation, that is, the helicopter will have increased range (headwinds aside) OEI.
Because of the enormous (and sometimes ill-informed) customer desire for "full CAT A", modern twins are being fitted with two huge engines that are each capable fo OEI flight across the weight range of the helicopter. To achieve this, the engines run at a low power setting when AEO, and thus are running very innefficiently. The lack of range in the AW139 is testament to this issue.
An engine left at idle will, however, burn more fuel than that saved by the more efficient power setting of the one left taking the load. So dont do it to increase range in a ferry flight. If you are in an emergency situation and running short of fuel with no where to land, you will increase your range by shutting down one of the donks - though make sure the wind profile supports this as stronger headwinds will reverse the equation.
Why would I only do this in an emergency? despite all the engineering specs, etc, there have been too many stories of transmissions damaged by extended flight on one engine to make it worth considering unless life was at issue.