TLDR: Yes... However I cannot say for certain that the intricacies are all properly modelled by Black Square.
Long answer: Constant speed props are governed by oil pressure. When a constant speed twin engine prop is shut down (or loses oil pressure), the feathering spring, counter weights, and compressed nitrogen in the prop hub are all designed to push the prop towards the feathered position to help reduce drag with an engine failure in flight.
However, the engine cannot be started with a feathered prop since a coarse propeller blade has more drag (on the rotational axis) which is hard on the starter motor and adds resistance in starting.
To mitigate this, locking pins will activate with a normal shut down when the propeller rpm is less than around 950 rpm locking the blades into the fine position. If the locking pins do not activate caused by a shutdown at more than 950rpm, a reservoir of compressed oil is stored while the engine is running to help unfeather the propeller and allow for 1 attempted restart. However, this mitigation is only really effective in flight where the airflow aids in spinning the propeller up to speed allowing the engine to restart. On the ground maintenance would have to reset the locking pins through some means to allow the engine to be restarted.
*Note that once unfeathering in flight to restart, if the engine partially starts and dies again it may lock the propeller into the fine position and prevent it from being re-feathered, so an attempted restart is only recommended if the pilot is confident in knowing why the engine originally shut down.