Did they ever do a storyline where he ate a cat?

That was always controversial, unless you live in Ticino (CH).

However, actually I wait for an answer to your question.
All I remember is that the family cat once had to be freed from the microwave in which Alf locked her (for further processing, of course). 🙀​🔥​ 🤣​
Alas, it inspired some kids to do the same with their 'buddies'...and hit the start button. ☻