Back when I went to Europe, three+ years ago. I flew from Raleigh to Toronto and took an Icelandair (very nice airline, btw) to Iceland to make another Icelandair flight to Paris. When we arrived in Iceland the plane stopped, what seemed like a mile from the terminal. A few buses pulled up and transported us to a heavily under construction terminal. When inside the first stop was customs. There we met with a massive line because the security staff was on strike so it was just management processing everyone. Iceland is part of EU so that was the only custom stop until we got back to Fort Lauderdale a month later. Originally we had a very short window to catch that flight to Paris and my sister was flying in from NY where we would meet up in Iceland and travel together from there on. I am not a panic type of person, but, I honestly didn't know what to do if we got separated, she had all the reservation and prepaid information.
Long story, at least, short(er) Icelandair had to delay the departure until all the transferring passengers where through customs and ready to board. We still arrived in Paris at the scheduled time. Must have kicked the plane into passing gear.