IME, generally yes. You don't need to pay for your ticket with your JetBlue card. You just need your card linked to your TrueBlue account and you need to book when logged into your account. In fact, it will even show you during the booking process that you get a free checked bag.

This is in contrast to United where it is most definitely enforced, meaning if you don't either pay for your ticket in cash with your United card, or at least the taxes on a points booking, they will charge you to check a bag.