Is it ever possible that the graviation from the mass of kinetic rotational energy will overcome centrifugal force?
In some sense, the answer is trivially 'yes':
Due to spacetime curvature, there exist no circular orbits below $\frac{3}{2}r_s$, with $r_s$ the Schwarzschild radius.
So whenever you get an object sufficiently dense, that its radius is below its $\frac{3}{2}r_s$, the mass equivalent to any nonzero rotational energy overcomes the centrifugal force of an orbit at $\frac{3}{2}r_s$.
Below $\frac{3}{2}r_s$ even zero rotational energy overcomes the centrifugal force, since the latter is then pointing inward.

This doesn't require a Black Hole.