Just daydreaming about it , I really see no huge structural strength by adding the cloth.
You should do a small test so you canFEELthe difference. Add some fiberglass to the top and bottom of a sheet of 1/8 balsa, let cure, and twist/bend it. Do the same test without the fiberglass. While you may no be able to see it....you can definately feel it.
The resin functions as a matrix. It's purpose is to transfer the loads to the fiberglass fibers. The tensile strength of laminating epoxy is around 10,000 psi. The tensile stength of fiberglass reinforced epoxy is around 63,000 psi (fabric is 0/90 to the loading axis, 50:50 fiber to resin ratio by volume). Fiberglass reinforced epoxy is 6 times stronger than just the raw resin. If you look a Uni-directional fibers aligned with the loading axis in epoxy you see that it 14.5 times stronger than just the raw epoxy. In respect to compression, the added uni-directional fiber will make the resin 5.4 times stronger. When you look at the Youngs modulus (translates to stiffness) you see that epoxy by its self is around 475,000 psi. Fiberglass reinforced epoxy is around 3,600,000 psi (fabric 0/90 to the loading axis). This means that the epoxy is 7.5x stiffer with the fiber than without it.
It's important to remember that fibers perform best when they are oriented with the loading axis.
There is a reason why structures are created with fiber reinforced polymers not just the polymer.