Has there ever been a diesel-electric helicopter?
Helicopters currently use lightweight but fairly inefficient gas turbines. Diesel-electric engines have great energy efficiency, in terms of mechanical energy delivered per kilo of fuel. However, they're quite heavy. This means that you need more lift, which in turn means more power is needed. This negates the initial advantage. 

With the advent of lightweight materials, the latter effect decreases so this situation might change.

Diesel engines can throttle up and down quite a bit, unlike gas turbines,  but this capacity is irrelevant to helicopters. Note that helicopters need a pretty constant amount of lift.