It's rarer for a ship to dock significantly late than it is to arrive at its scheduled time. Yes, it does happen, weather or issues in port. Thousands of ships dock everyday, a few will undoubtedly be late. Experienced excursion companies will be aware of your arrival.
On our recent European sailing with multiple embarkation ports there were separate gangways for embarkation passengers. On our final day we didn't disembark until 1pm. We needed to vacate the cabin at the assigned time in the morning and our luggage went out the night before. We just collected it from the collection point in the terminal once we'd disembarked.