The box is clever enough to know it's recording something. The display will show the clock, but if you look closely, you will see a REC 'icon'. You will also be able to hear the HDD making a slight noise.
EDIT: I have re-read you question. The unit must have power to it to operate. If by power off you mean unplug or turn the switch off at the back than obviously it won't do anything! If, however, you mean place the unit in standby by touching the big button in the middle, then the unit will wake to record a timer set recording no problem. As stated above, if a recording is in progress when you touch the centre button, the unit will go to standby but continue to record.
The HDR will display the clock when in standby.
