I'm not 100% certain of what you are trying to do, but if my guess is correct, this approach will probably not work.
I haven't done a detailed analysis, but my quick-look understanding of the "constant current" circuit that you posted is that it requires a resistive load to do its thing - the sense resistor and load form a voltage divider. The voltage regulator adjusts its output voltage depending on the current flowing through the sense resistor (within the scope of its "headroom"). That current flows because the load is connected and drawing current. If the load is disconnected, no current can flow.
If you plan to drive a stepper motor winding, it will act as anything but a straight resistive load. Rather, the winding combines both inductive and resistive components, and to top it off, you will be switching the winding on and off in order to put the motor through its paces. I'm not sure how you intend to do the switching, but you are probably going to have a very difficult time pumping a constant current through an inductive load that gets turned on and off with this circuit. You might even find that the circuit causes the regulator to go into oscillation.
So, I doubt that this circuit is what you are looking for in this application. But maybe some creative modifications would be promising.