Yes, airlines can change their delayed departure to on-time and depart the flight as scheduled. They can also reinstate flights that were previously canceled. It is not a common occurrence though, airlines know the trouble that it can cause for their passengers.
You must be checked in and available to board at the gate well in advance of your scheduled departure time. Please be aware that flight status can change at any time, and that delayed flights could depart on time if conditions allow it. Gate information can change without advance notice. Check flight information screens at the airport for the most recent gate updates. If you have questions, check with the airline.