Yes, a coral snake can kill a domestic cat. In fact the excellent reference work I have says: “Some cats will survive [a coral snake bite]“.
I don’t know what percentage of domestic cats survive a coral snake bite but the quoted sentence above indicates less than 50% and probably nearer a 30% survival rate. I’d welcome input from visitors. In an Australian study on snake bites (I don’t have more details) 91% of cats survived following antivenin treatment and 66% survived without antivenin.
The coral snake is quite small at less than three feet in length. It has a small head and a black nose. There are brightly coloured alternating bands of red, yellow and black down the body. The fangs on the upper jaw are not retractable.
The site of the bite will swell and become red but less so than for some other snakes native to America. The cat will feel mild to excruciating pain depending on whether venom was injected or not. There will be fang marks.
As the snake’s venom is a neurotoxin (toxin which poisons and damages the nervous system) the bitten cat will be weak and become paralysed. Other signs include: vomiting, urinary incontinence, convulsions, diarrhoea and coma. As mentioned some cats will die.
There is an antivenin for coral snake venom. The website: wagwalking.com (referring to dogs) states that the antivenin is not always available and sometimes ineffective. The cat will have to be hospitalised.
In the US coral snakes are found in fragmented locations in the the southern coastal plain from North Carolina to Louisiana, including all of Florida. Coral snakes are not aggressive and not prone to biting but will do so when necessary. It is most likely that the cat will be bitten on the face, perhaps the lip.
Primary reference work referred to: Cat Owner’s Home Veterinary Handbook, written by American vets who have first hand experience of these sorts of emergencies. And Wikipedia and vetbook.org.