Is it possible for a panel to arm/disarm itself without Customer Website arming schedules?

Yes. The Interlogix Concord 4, Interlogix NX, DSC PowerSeries Neo/Pro, DSC PowerSeries (for SEM), and Honeywell/ADEMCO Vista panels have arming schedules as a panel feature that can function locally. It is recommended to use schedules configured on the Alarm.com customer website because it provides the exact times of the schedule and makes them easier to configure remotely and troubleshoot.

Note: The Interlogix NX panels show User 97 armed or disarmed for local schedules.

For more information about arming schedules on Alarm.com, see Create arming schedules.