When a cylinder misfires, the fuel is not burned and is dumped out the exhaust. Over time this can damage the converter because the fuel is going to burn in the manifold or converter, and the increased temperatures are hard on it. This happens 100% of the time if left unchecked, but I've never heard of it happening anywhere near this quickly. It takes quite a while to slag the converter in an older car badly enough to throw a P0420 or P0430 trouble code.
But misfires and converters are related.
And it does state in the manual that driving with misfire condition can cause damage to CAT. In my case I drove the car all of about 3 miles with the misfire going on, but still had enough power after I got home to get it on the flatbed to haul to dealer. And it was giving off a strange smell which was probably from what you explained. Dealer drove it next day and said it wasn't throwing ANY codes, no exhaust smell, but showed history of misfire occurrence ? One week now and still waiting for the backordered converter.