Yes, the birthday child would be counted as one of the party jumpers.
If they have a membership and it's redeemable the day of the party, they can just check in using their membership and still jump with the party. Guests who check in using a membership are not counted as a party jumper which influences the total amount of pizza and drinks. They also will not receive any of the things provided for the party jumpers such as grip socks or ice cream, if applicable.