the monster mud is incredibly heavy and water-resistant but not waterproof in my opinion. Plus, heavy wet burlap alone would make your reaper look like cardboard cutout. So yes, chicken wire is necessary if you want it to look like a real being.
I'm really just interested in making this prop for a movie, not for being weather resistant or for a home haunt. Monster mud and chicken wire would be too heavy for my purposes. I'm wondering if I could achieve a similar result with paper mache, etc.