Yes, you can add a handler for the NRF_EVT_POWER_FAILURE_WARNING to your system event handler to deal with what you want to do when power is failing. You do have to do some configuration to make this event available to you. Take a look at the sd_power_pof_threshold_set function and its associated documentation.
We use this to handle when the battery in our device is getting to it's exhaust point so we can shut the system down gracefully. I don't know if it's fast enough for the case where you just yank power from you device.
