Can lidocaine w/prilocaine-topical cream be used topically over an ankle sprain?

Technically, yes: But you really shouldn't. Pain is a necessary feedback mechanism to keep you from doing things on an injury that you shouldn't. Numbing the ankle will only make you more liable to injure it more severely. As it is, ankle sprain causes nerve damage to proprioception (position sense) that results in you to twisting your ankle more frequently because the nerve feedback isn't there.

Not very effective: It could be used but I have not found it to be effective, as it does not penetrate the skin very well and will not get deep into the tissue. Anti inflamatory medication might be better for pain and swelling.