Good question.
I'd suppose wet muffler packing would be a bad, bad thing. How would you dry it out? Would you want to rinse it in place? Would that put the pipe at risk for further rust to develop?
I think I'd remove the baffle and packing, remove the packing from the baffle. Soak the pipe and baffle separately. When done, rinse, dry with a heat gun or leave out in the sun. Then spray the baffle and interior of the pipe with high-temp paint, maybe more than one coat.
Then re-wrap the baffle and reassemble with pop rivets.