Rotational and turbulent motion cannot "deepen" the gravity well in a galaxy of galaxy cluster. The contribution of kinetic energy to the stress-energy tensor is negligible compared to the rest-mass energy in non-relativistic systems.
Assuming you mean something like, 'how does rotational and turbulent motion contribute to the equilibrium configuration of a dynamical system?' --- then the answer is that they do contribute support against collapse. People are usually pretty sloppy in the terminology, but I think, the rotational motion would go towards "rotational support" (via centrifugal terms) and the turbulent motion would generally be grouped into "thermal support"*.
*For gas-motion scale turbulence this is a good, appropriate terminology. But for stellar motion (radial and epicyclic motion, etc) it is more based on analogy to thermal terms in the equilibrium equations.