The rule is 15-20 minutes, but it will vary by restaurant. I imagine if they have a large volume of walk-ups, they would be likely to seat someone who has already been waiting.
The ADR system doesn't work like regular reservations. You receive the "next available" table for your party size after you check in. If you don't check in around your ADR time, then you risk too many others, who have ADR times after yours, checking in. They will then be entitled to the next available table. It would make sense for walk ups to be filtered in between people who have ADRs, so if you miss your ADR and the next group with your party size has not checked in yet, they would put a walk up at your table. That's just how I see it working.
In short, if you want to keep your ADR, get there on time. If your son sleeps in during the first few days of your trip, then call and attempt to change the ADRs to later in the day.
In general, the first few ADRs of the day have the most flexibility, so even if you miss your ADR, they would be more likely to be able to accommodate you into a later time, but there's no guarantee that this will happen.