I wouldn't expect so, but I'm not sure. Bulk metals like steel and aluminum can support stresses in both tension and compression, so they can maintain their integrity when bending loads are applied such as when pedaling.

I'm sure carbon fibers will want to buckle when in compression though they are phenomenal in tension. Problem is how can a slender one be designed to stay together under those loads?

Makes me wonder why a carbon fiber can't be made with a, let's say, 15 mm diameter?