If by "algorithm" you mean a fixed sequence of moves, then the (rusty math alert) I'd think the answer is "no", because then that algorithm would be an element

If by "algorithm" you mean a fixed sequence of moves, then the (rusty math alert) I'd think the answer is "no", because then that algorithm would be an element of the Rubik's cube group, which you could apply compose repeatedly with any other element to get the identity. This would imply that the Rubik's cube group is cyclic, and I don't think it is (because it's non-Abelian).