I don't know how service is on the East coast, but over here assume the train will be running 10 minutes late for each stop it's made since it's initial start. Yes, that means that it's about 8 hours late by the time it reaches Seattle from San Diego.
Anyway, your train isn't likely to be at the station more than 30 minutes before it's scheduled to leave. Check in took very little time.

Or you could call the local station and ask :).