Haskell, 93 88 86 bytes
any(all(\(a,b:c)->1>mod(a!!1-b)4).(zip=<<tail)).mapM((\a->[a,a+1],[a+1,a]]).read.pure)
The last line evaluates to an anonymous function. Test suite here.
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.