Ignoring the behaviour of the energised coils causing back-emf when disconnected (Jazz's reply) - there's another issue at play here - the stepper drivers would have their own instance of the X/Y coil phasing - swapping between controllers would introduce a discrete change in motor armature position - which I would expect is not desired. That and blowing up the drivers.

As previously explained - use a control system that allows the step/dir to be multiplexed. If using open-collector drives it's possible to wire-or the cathodes on the driver step/dir inputs.