Whatever you think this airport is, go smaller. Imagine entering a backyard, with a shed between you and the yard is surrounded by chain link fencing. Inside the shed, which is well-maintained and clean for a shed, there is no US customs, and I would be shocked if it ever will happen. There is also a desk and a metal detector and once you're through the detector you're outside of the shed again. The airport must serve hundreds of people every year. The plane will arrive anywhere between 15 and 90 minutes late, make lots of noise, drop off some people and pick up some people in a short turnaround. I would recommend arriving at least 5 minutes before your flight is scheduled to depart.
In all seriousness, unless there's a bag check cutoff, as long as you're within screaming distance of the plane (before or after security), they won't leave without you.
The block party is fun (look for fish fry in Gov. Harbour on maps--I think it's on Fridays), and French Leave Beach is outstanding.