You ask about using the billhook as a draw knife. Not the greatest.
The problem is that the billhook edge has a bevel on both sides so it won't "ride" on the wood as easily as a single bevel does..
I expect that it will tend to dive in quite easily.
You should be able to learn to use it as a draw knife with some practice.
The time of year and thus how tight the bark is will have some bearing on performance.
I use a Stubai drawknife to peel the sapwood off large pieces of western red cedar for carvings.
Must admit that being able to use both hands to steer the blade is another advantage.
You will be cutting with pull strokes.
If/when that blade jumps out of the wood, it's coming towards you very quickly.
Better make a defensive plan right now.