It is likely to depend on the agent checking you in. I once walked up to the counter 2 hours before my scheduled departure time only to be told that I couldn't check my bag because my flight wasn't leaving for 5(?) hours. I had no idea the flight had been delayed and pointed out to the agent that I was checking in based on the scheduled departure. They went ahead and checked my bag.

I'm sure that there would be times when I would have been told to just wait (outside of security) until the window opened for the new departure time.