Not really sure why I'm wading into this, but this happened to us a few years back, and yes, they opened the gate. We left for the airport in what should have been plenty of time, but it was one of those mornings when everything went wrong, including (among other things) a very long line at security and a ridiculously long line at customs (US pre-clearance). When my family finally made it to the gate, it was closed. The plane was still there. Another passenger came up just behind us. There was an airline employee heading down to the airplane who saw us arrive. The gate agent was in the process of rebooking us when the employee came back, stuck her head through the door, and said "the pilot says to let them board."
I think they figured it would take longer to pull our checked bags than to board us. We were very fortunate, and obviously wouldn't have blamed the airline if we'd missed it. But even this is not absolute.