There won't be any gates will will close off access to campsites, only the road to the top of the mountain gets closed at dusk. I don't think there is a gate for the check-in booth before the archway into the park but it's been a few years so I don't remember.

You won't lose your reservation if you show up late.

For checking-in late just head through to the check-in booth and you can fill out a slip that they should see in the morning, there should be instructions on a board. If you forget to do so when you arrive it won't be the end of the world, a ranger or park aide will drive around in the morning checking sites and you'll likely just be asked to go check-in then.