A wooden bat no. A real bat, why would you eat that in the first place? If cooked long enough I'm sure any disease would burn off but no quite positive I never tried it. Tell me how it goes for you.
If the bat in question as rabies you can consider it poisonous.
Rabies vaccinations in cats need to be renewed every 1 to 3 years. Your cat shouldn't contract rabies if they've been recently vaccinated. If you think your cat has been exposed to rabies, or can't remember when your cat was last vaccinated, call your vet ASAP. There is no cure or treatment for rabies in cats once symptoms occur, it's a fatal disease. It's also a disease that humans can contract. Unfortunately, there are no tests that definitively show if an animal has rabies except for a test that is performed on samples of the brain after the animal has died. This is why it's extremely important to keep up with your cat's rabies vaccinations.
Only if the skunk has rabies.
The bat
A cat can get rabies from any animal with rabies, either by being bitten or saliva. even eating an animal that has rabies. WARNING: IF you have come into contact with any animal that has rabies even before it was showing "signs" please please please go to your doctor and let them know so you don't die or transmit it to anyone else. Most warmblooded mammals that are not vaccinated, including cats, bats, skunks and ferrets, can contract rabies. Like dogs, cats should be vaccinated regularly according to local laws.
Rabies
There is no specific type or class of bat that has rabies; just be on careful alert and keep clean to avoid rabies.
Most deaths from rabies in the United States result from bat bites
Rabies is transmitted through the salvia. If a cat has rabies, he can infect you with it. If a person is bitten or scratched by a cat with rabies, they have the possibility of getting rabies. An animal with rabies can show several symptoms. It can be disoriented, dumb looking, vicious, tired, foaming at the mouth, and/or unable to swallow. The only way to check for rabies is to send the head of the animal off for brain biopsy. For humans there is no test. If you are bitten or scratched by a rabies animal, go get rabies shots immediately.
no it's dead
It is unlikely. Rabies is caught by the transfer of bodily fluids, and if an infected cat bites you, you may get rabies from his saliva. In order to catch rabies from a cat scratch, the cat must have bodily fluids on his claws, which is unlikely unless his feet are bleeding for some reason. If a cat gets into a fight with a rabid cat, and then scratches you when you try to separate them, it is possible that the rabid cat's blood can get into the scratch.
rabies