Short answer
Yes, even a small lick can cause diarrhea or vomiting in a cat. Energy drinks contain caffeine and high sugar, which are very hard on a cat's digestive system. The bigger danger is that caffeine is toxic to cats and can cause heart problems. If your cat licked any amount, call your vet or the ASPCA Animal Poison Control Center at (888) 426-4435 right away for advice.
Energy drinks — Food safety facts
Do not feed · Cats · full breakdown on the linked food page
Caffeine, taurine and sugar together — a cardiac emergency in small pets.
The full verdict, portion guidance and serving notes are collected on the Energy drinks food facts page.