Not necessarily. The signature has traditionally served two different purposes: 1) to confirm your identity and 2) as an agreement to pay the card issuer. With Apple Pay, confirming your identity is moot but they may still want the signature as an agreement to pay the card issuer. In fact,
Apple support page on Apple Pay says the following:
The first two times I used Apple Pay at Petco, they didn't ask for my signature. The third time I used it when the transaction amount was over $200, they did ask for it.