No, but here's what would happen if you tried:
Carbon fiber is very strong for its volume, so if you go and calculate the amount you need to make a strong fuselage ignoring the local strength you need to keep the sides from caving in, you come up with "not much". Then you make your fuselage, and as soon as you pick it up the sides under your thumbs go "bworp*" and cave in. To see this effect, pick up an empty pop can and squeeze gently.
So you make the sides with two or three layers: either one layer of CF with enough balsa inside to prevent the "bworp", or CF, balsa or foam, then CF, with each CF layer being half of what you used in the "bworp" example. Result: a fuselage that is strong in all ways**, light, and insanely more difficult to build than just using balsa.
*
http://en.wikipedia.org/wiki/Don_Martin_%28cartoonist%29** when you squeeze it it will go "fleen", but silently because it is not moving.