Everyone counts on an ADR, regardless of age. If someone gave birth, picked up the kid and went directly to a character meal, they'd need to have the baby on the reservation.
Not that if the baby wasn't included the party would automatically be turned away, because they probably wouldn't - but if a party of four arrives as a party of four plus a baby, they'll go down as a party of five. If the restaurant is at capacity and can't accommodate a party of five (yes, that happens sometimes, although not often) then they'll be turned away or someone (probably not the baby) will have to sit out.