I did the exact some thing in Mystic, CT. They give you certificate to mail into the state and you pay an additional fee. The state will mail you your card.
This is pretty much standard with any class you take in CT to get the card.
Not that I'm a great lover of jet skis, but, I sometimes regret that I didn't get the PWC endorsement as there have been a couple of times over the years that I could have hopped on a friends jet ski and taken it for a spin