There have been many delays at the airport where I work due to backups and delays in Immigration and Customs. We will rebook you if you miss your flight, but we are supposed to book you on flights with award availability if you booked tickets using miles. A customer service agent at the counter can’t open up award seats for you. You’d have to call MileagePlus. But, the goal is to get you where you’re going, so you never know what will happen.
I would add most flights are full, so keep that in mind. Not much availability to rebook and it’s predicted to just get worse this summer.