One at idle? This would most likely result in an overall increase in fuel consumption, not a saving. At idle a turbine engine consumes a considerable amount of fuel for no useful output to the transmission - it would disengage.
Think OEI transmission limits, this isn't an emergency so normal limits would apply, resulting in a reduced cruise speed.
For example, normal cruise Tqs = 80/80% = 160% total.
When OEI, 100%/0% = 100% total.
If flying into a headwind, the range might be considerably reduced.
If one engine were completely shut down, the extra "idle" fuel wouldn't be consumed but the OEI limits still apply. Again, the headwind would need to be considered. Endurance would be increased, but possibly not range.