Lmao!! 
Pure genius!
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Interesting question. When i was a kid, our HS assistant librarian encased a tropical fish in a resin block. After about five months, the (extremely hard, fully-set) resin cracked from the pressure of the decay-gases. And it was only a 1.5 inch long fish!
Maybe vacuum-freezedrying?
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Wont the fluffy look all weird and desiccated?
If it were freeze-dried in an airless vacuum chamber, not likely. Some museums have animals on display that were freeze-dried rather than stuffed. They needed a touch of paint here an there as well as new eyeballs & such, but not much more than that.
I think you’re right, they would rot. To be honest, I don’t really know much about resin, I’ve never done it myself. I think @Guodzilla is right, and they would have to be dried in some way.