LM317/338 constant current open circuit
You are correct - the output of your regulator can not exceed the input.
What the 'constant current' source will do is TRY to maintain a constant current.  It does this by adjusting the output voltage such that it's driving the program current.
You won't have a 'spectacular failure of the device' if you startup with no load.  If anything, the regulator will be very happy to remain in that state indefinitely as it's basically doing no work.