I agree with Lucas. If you don't have any knowledge about your starting position, and you make eight moves, you still have no knowledge about your ending position.
A random position is highly unlikely to be within 8 moves of being solved. But if you make the assumption that your are certain that it is not within 8 moves of the solved position, then you know something about that position, and the assumption of it being a completely random position is false.
Without that assumption, then you have that there is a small probability that it is within 8 moves of the solved state, and there's a small chance that some chosen 8 moves will solve it. The end result is still a 1 in 43 quintillion chance (approximately, of course) of the ending position being a solved cube.
The Cayley graph for Rubik's (for face turns, let's say) looks exactly the same from any node. Because of that symmetry, you can't pick a set of moves that will tend to favor one position with respect to others.