Most turboprops are capable of starting engines with battery power only for the starter. Some of the medium size ones like the Dash-8 may have an APU, but the APU isn't required to start the engine. On the big turboprops such as the C-130 with Allison's, I think you will find that an APU is required because those starters need air to turn them over. Lose the APU and you are not going anywhere without a ground air supply.
Anybody know what is required for the Transall or the Britannia?