I have no hesitation in using a 1/32 ring with an 1/8 chain, but I would always use a 1/8 sprocket.
12 is a very small sprocket. It won't run as well as a larger one. I only ever used a 12 for roller record attempts, and it was critical to get the line right if the chain wasn't likely to try to climb off. As has been identified, the angle between the teeth is much greater on a small sprocket. The chain will also have to go through more movement, which adds wear and is less efficient.