[jtms]

Would this system be legal in professional competition cycling?

[joerickard]

No, this violates current UCI rules.

"The front wheel shall be steerable; the rear wheel shall be driven through a system comprising pedals and a chain"

However, the rules do change and have been recently (like the removal of the 3:1 restriction).

[notatoad]

Probably not, the UCI operates on a policy of all new tech being forbidden until explicitly authorized.