The power supplies used in PC's are switching power supplies. This means they need a load (such as your HD's) in order to work properly. I've used old PC power supplies to operate a variety of devices without a problem. The only concern I would have in your case would be if you are using the PS to operate drives that are going to be connected (I’m assuming) to another computer with a separate PS that they would not be sharing a power ground. This might cause you some problems, anything from it just won't work, to possible damage to your hardware, it might also work just fine. If you are not <b><i>absolutely sure </i></b>of what you are doing, <b><i>don't play with power supplies</i></b>, the voltage output is rather low (usually +12V, +5V, and -12V) but they are capable of several amps, meaning things can get real hot, real fast, and the results could cause you injury.
I'm curious, what kind of arrangement are you looking to create?
It probably won't work. Most newer computers use ATX power supplies which require the motherboard to send a signal to the power supply telling the power supply to turn on. Without the motherboard functioning there is nothing to send the signal from the power switch to the power supply.