It might, depending on the requirements of the device.

NiCd ("NiCad") and NiMH (nickel metal hydride) batteries have a characteristic voltage of about 1.2 volts per cell, and when you charge them fully, you can measure perhaps 1.4 volts on the cell.

When you discharge these batteries by using them, the peak voltage of 1.3 to 1.4 volts per cells drops off rather quickly, and then you have a battery that from about 85% charge down to about 15% charge, is delivering about 1.2 volts.

At the point when the voltage drops below 1.2 volts, the battery goes dead rather quickly. NiMH cells especially drop their voltage very, very fast below 1.2 volts.

Here's a very nicely written paper on NiMH rechargeable batteries:

http://www.hardingenergy.com/pdfs/NiMH.pdf

Here's a general overview paper on NiCD, NiMH and LiON batteries:

http://www.national.com/appinfo/power/files/f19.pdf

Here's the discharge curves on Duracell batteries:

http://www.duracell.com/oem/primary/alkaline/alkvoltage.asp

By looking at all the curves, you see that even the one-shot Duracell type batteries don't spend a lot of their life at 1.5V. I've run into devices that really want 1.5V cells, and when they quit functioning, the AA's (or whatever size batteries) I pull out of these devices have quite a lot of life left in them.