Stuff like this will definitely happen. The thing I tell my team is that "Train Wrecks" will happen and if we expect them, then when they do we won't panic and we can do our best to navigate them well.
2 weeks ago we had a new guy on the sound board, we were introducing the song "God of the Promise" by Elevation and the new guy forgot to unmute the click during the stage transition. So in our ears we had the guide and the track but no click. So the drummer attempted to salvage it but we were WAY OFF. 3-4 seconds in, I just laughed and said "You know what, can we start over? Hey Rob, (new sound guy is also Rob) can you unmute the click? Thanks man, This is a great new song we want to share with you guys!"
We then launched into it again and it went great!