Yes, black widow spiders can kill cats. The stings of black widow, brown recluse spiders and tarantulas are toxic to animals. The bitten cat will feel a sharp pain at the stings site.
Later the cat may develop labored breathing, fever, chills and excitability. He may then go into shock and seizures may occur. There may be early paralysis from a black widow spider bite. Most cats will die. Therefore, the corollary is that some cats will survive; death from a black widow spider bite is not 100% certain.
There is an antivenom (antivenin) for a black widow bite. Obviously it has to be obtained from your veterinarian in time to save your cat.
Because free-roaming cats are able to express their desire to hunt and also because they are curious by nature they tend to be at risk from poisonous insects. Cats tend to get stung about the face and the paws.
The Northern black widow spider is primarily found in the north-eastern United States. I’m told that they may also live as far south as Florida and as far north as Canada and going west they can be found in Texas as well.