I haven't got around to trying it with muzzleloaders because I'm using them in "closer" country and taking shorter shots. But with cartridge guns and more open country I usually carry a walking staff in honor of our really steep country and shoulder-high grass. My experience with staffs and sticks is therefore with modern guns, but I've always "assumed" it was transferable to muzzleloaders. I know, I know.... ass-u-me.
But here's what I found in some serious testing. Shooting while standing, using the staff for a rest roughly doubles my offhand range, or in the case of huffing and puffing, lets me shoot at my normal offhand distances long before my lungs catch up with my body. I can tame the swaying and wobbling enough to allow fairly quick "offhand" shots without waiting till I've recovered from a climb. With our tall, tall grass there's often zero opportunity for prone or sitting shots, much less for kneeling shots.
When I can manage a sitting shot, shooting with the staff is virtually as effective as shooting prone with my rifle on a rest. It's downright amazing just how steady you can be sitting and shooting with a staff.
POI certainly does change if you clasp the rifle tight to the staff. I get zero change in POI if I rest the rifle on top of the hand clasping the staff, or at most raise my thumb to create a "U" into which my rifle drops freely. Choice between those two depends on terrain and angle of shot. But the minute you squeeze the rifle up against the staff, POI can shift a lot.
As I said, none of this is confirmed with a muzzleloader. But it would take actual shooting to change my mind about applying it to muzzleloaders, too.
Edit: One big WOOPS in all this. Our ground is generally soft. My staffs are all mildly pointed and I can shove them into the ground a bit before using them for shooting. That's the big difference in their effectiveness as shooting aids.
