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Play it safe or be adventurous and possibly unique?
No, I've never used cedar for a structural part (besides bridges). But I looked up the numbers below and think that the whole banjo could be yellow cedar.
online quotes of physical properties:
property - Alaskan yellow cedar - Honduran mahogany
___________________________________________
weight - 31 lbs/ft^3 - 37 lbs/ft^3
elastic modulus - 9.8 GPa - 10.0 GPa
Janka hardness - 580 lbf - 900 lbf
Made into a neck or a rim, the cedar would wiggle (i.e., sound) rather like mahogany because of the similar weight and stiffness and be similarly strong. (It would be easier to dent and would need a hard fret board.)
Yellow cedar is said to be dimensionally stable and easy to work. The yellow eventually turns to grey. As a "soft wood," it won't bend like hardwoods. So, a block rim sounds plausible. On the other hand, this guy does dramatic bends with steam and claims to do cedar, too: https://www.tomraffield.com/en-us/blogs/blog/steam-bending-q-a-with-our-workshop-team . (I guess you'd just need extra -- to make up for the ones that split in the process.)
A neck can have a truss rod and/or be pieced out of flipped-grain boards. Rims are a bit mysterious (https://www.its.caltech.edu/~politzer/rims/rims.pdf), e.g., how thin light ones turn out to sound not that different from heavy, stiff ones.