## Haskell, <s>93 88</s> 87 bytes

    any(all(\(a,b:c)->1>mod(a!!1-b)4).(zip=<<tail)).mapM((\a->[[a,a+1],[a+1,a]]).read.pure)

This evaluates to an anonymous function that takes a string and returns a boolean. [Test suite here.](http://ideone.com/mVASck)

## Explanation

The idea is that the lambda on the right maps a number `a` to `[[a,a+1],[a+1,a]]`, the two possible "moves" that take the crank over that number, according to the following diagram:

      1 (2) 2

    (1/5)  (3)

      4 (4) 3

In the main anonymous function, we first do `mapM((...).read.pure)`, which converts each character to an integer, applies the above lambda to it, and chooses one of the two moves, returning the list of all resulting move sequences.
Then, we check if any of these sequences has the property that the second number of each move equals the first number of the next modulo 4, which means that it's a physically possible sequence.
To do this, we `zip` each move sequence with its `tail`, check the condition for `all` the pairs, and see if `any` sequence evaluates to `True`.