Fast charging is controlled by the phone's software, so I would expect power-on to be necessary. If you power-off during charging I would expect the device should stop charging, or shift to a safe minimum default charging current which will not allow the battery to be overcharged under any circumstances.
Note that an overcharged Lithium Battery can go into thermal runaway and result in an unplanned meeting with your local FireFighters. My advice is to leave the phone powered ON while it charges so the software can safely control charging. If you don't want it disturbing you during charging use the Silent switch or the new Focus function (Used to be Do Not Disturb).