F3G,
If my memory serves me right, and I am fairly sure it does (I used to instruct on them) the Bulldog prop goes to coarse if left to its own devices.
One relevant incident I remember occurred to a solo student at RAF Cosford in the early 1990s. He landed long, and bounced a couple of times, making a heavy landing on the nose wheel. This caused the nose oleo to be pushed vertically upwards, damaging the constant speed unit on the back of the engine (take a look how close the CSU sits above the top of the oleo - it's very close).
This allowed the prop to go fully coarse.
He tried to go around but the engine wouldn't pull against the coarse pitch and he couldn't climb. He was very lucky to make a survivable forced landing off the airfield.
If, as you have intimated, you fly a Bulldog it is worth remembering this if you ever suspect you have dinged the nosewheel. It's much safer to close the throttle and leave it on the ground.
As I always used to teach, mainwheels are for landing on, nosewheels are for steering only.
ShyT