[SkunkBoat]

CarbonCore weighs about the same as AB grade douglas fir plywood. It is made with polyester resin and filler "micro-beads" to make it lightweight.
A good thing is that is completely fills the stringer space. If you use wood you have to use polyester filler to avoid gaps.

Yes the strength is from the sandwich of the glass with the core, whether its plywood, balsa, foam or other. The bond is important. If the bond between the sandwich is lost, it loses most of its strength.
You can't just stuff it with dry foam and you need a pourable foam that bonds with the glass/poly resin. Or maybe there is a brand of sheet foam that can be glassed like a piece of lumber and then glassed into the hollowed out stringer space? hmmm...?

I like that the CarbonCore (Arjay/NidaCore) does not soak up water. If you use the closed cell foam it will eventually soak up water. How much and how quickly depends on a lot of variables. Same with wood. All it takes is one screw hole or a bilge drain pass through that isn't glassed(the main problem on V20s)

The insulated fish box on the V20 is a good example. It is glass over foam. Mine was completely soaked due to years of water thru screw holes. The glass separated from the foam and the floor of the fish box was flimsy.