Certification requirements definately require feathering of the propeller, whether it be manually or by auto-feather.
In a piston engined aircraft you might get away with waiting for 400 feet before feathering, if you were at very light weights.
Any engine which drives a propeller must produce sufficient power to meet it's own internal requirements, and the balance available supplied to the propeller. If the engine fails, the propeller now extracts from the airstream that power required to meet the engines internal requirements.
A piston engine requires about 10% of the power produced to meet it's internal requirements, a turbine engine requires about 2/3 of the power produced for 'itself', leaving 1/3 for the propeller.
If we consider a 1000 HP piston engine failed, the propeller will extract about 100 HP from the airstream. A 2 engined aircraft could probably maintain level flight, and a possible reduced climb.
If we consider a 1000 HP turbine engine failed, the propeller will extract about 2000 HP from the airstream. A 2 engined aircraft would be incapable of further flight (except downwards).
It is for this reason that many turbo-props have medium and high propeller stops, to hold the propeller at a high, low drag angle in the event of windmilling. These stops would invariably not be reached during takeoff, only later in the climb or cruise regime.