You wouldn't be shutting one down for a 25 minute Medevac, but on longer offshore flights it could be beneficial.
"Good morning everyone. Now that we are safely offshore and only have 120nm to go to the rig, please don't worry of you hear the engine note change. It just means that for eco purposes, we will be shutting one engine down. Don't worry, we will keep the other one as a spare, it will only take us a couple of minutes of autorotation (a bit like gliding) to re start it. If at any time you notice the rotors slowing down, please adopt the brace position and activate your re breathers. This means that the other engine (the non spare one) has stopped and we didn't react quickly enough so we will be ditching. In the unlikely event of this happening, the landing maybe slightly firmer than normal on the water. Thanks for listening, now sit back and enjoy the flight and we will talk with you in a couple of hours, yes, the aircraft is a little slower when we don't use the spare engine"
What a great idea in the current climate of cost reductions. I will see if we can trial it on the 225 fleet.