Teeth Whitening on Decayed Teeth?

While it is "OK" to do it, there likely will be pain and discomfort if done. Whitening gel can wick moisture out of teeth and make them ache. Decay allows more "wicking" and result in pain.
The color of the decay won't change, so the end result is still a need for fillings or other restoration. In the case of large amounts of decay, it is not uncommon to place a temporary filling, bleach, then finish/redo the filling. If fillings currently exist but have decay, there shouldn't be much issue of simply bleaching and then replacing the fillings when complete.

Restoring decayed teeth is more important to your health than whitening and should be taken care of as soon as you can.  Once you have restored your decayed teeth and have gotten a professional cleaning, then you can go forth with whitening options.  However, keep in mind that dental fillings and crowns can not be whitened with whitening products.  Thus, there may be a shade discrepency when you whiten your teeth after placing your fillings and crowns, and this may be an esthetic concern for front teeth.  The sequence of your treatment plan will be discussed with your dentist after a thorough examination.  Best, Dr. Elizabeth Jahanian.

You really need to take care of basic dental problems, such as decay, before purely cosmetic issues like whitening. It's possible to need root canal treatment or even lose teeth if decay is extensive and treatment is delayed. If areas of decay are very small and not very deep, you could get away with whitening first, but I would worry it would be painful. Sensitivity is the most frequent complaint when whitening intact, healthy teeth. Whitening teeth with cavities of any size in them is really asking for a problem. 

I think that i became a dentist to help people take care of their teeth and keep them healthy first and foremost.  The second thing i would do is the cosmetic whitening the patient requested and i would do it that order. It would be less painful for the patient doing  the whitening last and ,honestly, the patient as well as the dentist need to make sure the teeth and gums are healthy before cosmetic work is done. 

Your back teeth will probably need to be filled first before any whitening is performed due to the sensitivity it could create. Front teeth can be whitened first because its easier to match the shade of the incisors if they have been whitened first. General rule of course, not carved in stone. Your dentist will let you know whats best.