Can digital clocks and other electronic devices "ride through" a momentary power interruption?
Its product dependent.

When the power is off, only thing that device can rely on is internal capacitors. Time that device may keep the voltage will depend on rated power, actual power consumption, and device topology.

Say, you are having a 5V 200A power supply. If you power a LED from it, it may stay lit for many seconds after power-off. In the other hand, if you put high load on the same power supply, reset may happen even if few cycles were missed.

Most of the devices have different capacitors for different power rails, in your case, there might be a capacitor that keeps clocks running for some time.

Even if you skip a few cycles, many devices will go crazy. You need to use UPS to prevent that