I did it! I halved the recipe and had to make self-rising flour since I don't have any. My recipe was:
1 c Kirkland Signature Super Premium Vanilla Ice Cream, softened (not fully to liquid, but softer than soft serve)
1 c AP flour
1 1/2 t baking powder
1/2 t salt
I wasn't sure if I was supposed to melt it all the way, so I just used the "soften: ice cream" option on my microwave. The resulting batter was too thick to pour but soft enough to spoon in. I only had mini cupcake papers, so I used a mini tin.
The end product was tasty, but not what I would call a cupcake. The texture and flavor were somewhere between a biscuit and a muffin. The outside was rough and crusty like a biscuit, the inside was soft, like some biscuits I've had, but really more like a muffin. It was also rather sweet for a biscuit, but not as sweet as a cupcake. Since they weren't very cupcake-y, I didn't bother frosting them (I was going to just use Nutella) and instead enjoyed a couple with strawberry freezer jam.
The KS Vanilla isn't a terribly sweet ice cream and it's much denser than the mainstream supermarket brands. Like others have said, I'm sure results vary drastically fron brand to brand. Also, I think the salt measurement in the recipe for self-rising flour was a little high and I probably should have made the flour and then measured out a cup. I don't think the extra 2 tsp of dry ingredients made a huge difference, but with this small of a batch, who knows. I also wonder if the texture might have been slightly different if I had melted the ice cream completely, especially since mini cupcakes cook so quickly.
Anyway, the "miscuits," as DH named them are tasty and I'm sure the sproutlets won't object to munching them tomorrow, but I think I'll skip the flour and just top the ice cream with Nutella next time.