Does a motor's stall current change with applied voltage?
Some motor basics.

A motor's stall current is determined by the resistance of the coil. (quoted at the nominal operating voltage). If the shaft is clamped so it cannot rotate then the 'motor' will act like any other resistor and follow Ohm's law - so yes, the stall current will increase with increasing applied voltage.

Once the rotor starts to rotate it will induce a back emf so the voltage 'seen' across the rotor will be reduced. The net current through the motor will be reduced. 

Increasing the applied voltage will increase the speed (how much depends on the motor). With increasing speed comes increasing loss (friction, windage etc.) so there will be a corresponding increase in current.

Applying a load (torque) to the output shaft slows the rotation speed and reduces the back emf. This in turn  will increase the motor current. Applying too much torque may reduce the shaft speed to 0 and this is once again back to a stall.