If the train is late 30 min will it arrive on time at other destinations

In a lot of cases the answer is yes because there is padding in the schedule especially going east into Albuquerque.

I just took the train from Gallup NM to Flagstaff AZ. And it was supposed to leave at 6:40pm and it didn't leave till 10pm. And I was meant to arrive in Flagstaff at 2am but didn't until 5am.

Sometimes

Sometimes it is able to get back on schedule, but yes it has been late for other stops if already behind.