It has to exist: it's a mindbogglingly large but finite number of possible permutations, and to go from any one permutation to any other takes a finite number of moves. Therefore, if you can enumerate all possible permutations in some way, any arbitrary way will do, you have a Devil's algorithm by going through them in that order. The question is not whether a Devil's algorithm exists but what the shortest one is.

Somewhat related: I was playing with cube recently, and, starting with solved state, I started doing sequence of two moves that came to my mind: rotate right side down, then the bottom, clockwise. After maybe a 100-150 repetitions (I did not count, just did the moves mindlessly for couple minutes) I went back to solved state. I wonder if there are more such sequences, and how long it takes to go back to original state. The obvious difference from Devil's algorithm was that the 2x2 sub-cube remained untouched the whole time, only the edges were messed up.