Can a motor driver for 5V be used for a 24V motor?
From the datasheet, the UNL2803A has a Vce (sustaining) of 50V. Provided that the max current for your 24V stepper is 500mA or less and you are careful with your grounding, it should work for you.  Be sure to only supply the motor and 2803 with +24V (and not the Arduino!).

EDIT:
Your circuit will look something like this.  Note that there is only one place where the 24V return and digital ground are connected together.  The 24V wiring will carry more current than the digital wiring; take this into consideration.  Also, Richman's comments about power dissipation are spot-on.  You'll need to take this into account as you select a motor.
(Apologies for the hack diagram)