Personally, I don't think it's a bad idea. People sometimes use pieces of white fish or even shrimp/prawns to cycle their tanks so I don't see any reason why not to cycle with the fish that have passed.
Plus, it's going to take anywhere from 3-6 weeks to cycle the tank so you can raise the temp to 90 degrees Fahrenheit or a little higher during this time and that will kill any Ich parasites.
Just make sure to find the skeletons afterward so it doesn't cause any issue with your filter propulsion.
EDIT: Okay, I should have read the rest of the comments. I always use fish flakes to cycle my tank. In fact I don't even put the flakes in the tank itself for the filter to suck some of it up, I place the flakes directly into the filter. It's much easier this way. After your water parameters are where they should be (Ammonia-0, Nitrite-0, Nitrate-approx. 20ppm) I would recommend placing another filter pad in with the old one for about 3 weeks and then remove the old one.