Of course cats can get food poisoning,
Cats can most definitely get sick from spoiled food-diarrhea, vomiting, the works. Depending on how serious the vomiting and diarrhea is, it may require immediate medical attention. I wouldn't let vomiting and diarrhea go on for more than a day w/out seeing a vet because dehydration is very very dangerous and requires IV fluids.
yes they certainly can.....has your kitty eaten something tainted?
please get him/her to a Vet clinic immediately....♥