Answer
No. There will be $^{14}C$ in both $CO$ and $CO_2$ after some time. Since the reaction never actually stops, there will be some $CO_2$ that was produced using $CO$.
Work Step by Step
At equilibrium, the reaction does not stop. The forward reaction is occurring at the same rate of the reverse reaction, but the molecules on that system are at dynamic equilibrium, reacting all the time. $CO$ are turning into $CO_2$, and vice-versa.
When that dynamic equilibrium occurs, the $^{14}C$ will be moving around $CO$ and $CO_2$ molecules.
