Best not tell that to Fascinating Aida...
No, they will be fine with it. They look like they understand formal logic.
Necessary means you can't have humour without repeating the c-word. Black Adder (and many others!) proves you can be funny without using that word.
Sufficient means that the c-word repeatedly is all you need to be funny. Kevin B. Wilson proves that you need more than that.
But neither implies that you can't be funny and say canute. Fascinating Aida and Derek & Clive (and Hit Girl) prove that you can.
Disclaimer: I would happily use that word in plain text, but CC would change it to daffodil. And I will get banned if I use Greek letters to get around the filter.