All of my Lyman Reloading Manuals and Cast Bullet Handbooks have rifle and pistol loading data for the 32-20, using available powders.
Yes, funny, Hornady shows Contender and Rifle data, but not revolver data.

. And Lee lists data, with the advisory "velocity will be higher in rifles" (implying its revolver pressure)?
Another post mentioned "rabbits not that hard to kill", and I agree in total. Any rifle velocity loads, will for sure kill quicker, and add a few yards capability.
Any that think velocity, even on small critters, is not more effective, has been shooting different small game, than I have.
From 17HM2, to 22 standard velocity rimfire, solid, to 22 HV HP, on up the scale higher velocity is more effective on small critters in particular.
Once into the center fire rounds, then for sure, a 17 Remington, will carry better than the 17 Bee, and "kill" further out, at the cost of twice the powder.
But back too the conversation, all things equal, no, the 32 20 rifle loads, would not add much, unless, the critter was at the 75-100 yard point.
And then, I would opine its conducive to the task.
But out to maybe 50 yards, where a lot of that shooting takes place, no, not much advantage over target loads, if using a good SWC bullet.
All of this commentary, pertains to the original question, effectiveness of a now near ancient pocket revolver round.
Somehow, the same effectiveness, or lack of effectiveness, applies, in what ever living target.
All said, if katy bars the door, I hope to have a scattergun close by.