I have seen no rechargeable device that requires the power switch that lets the device function turned on. Often, it is mentioned that the length of time for a full charge will be longer if the unit is in use at the time since the unit and recharging function both require power and if the player is in use, it logically has priority over the recharging function. In other words, it should charge more quickly if the player is turned off.
Unfortunately, Initial's website: http://initialdvd.com/ is no longer in operation so finding the manual could be a problem. Initial Technology has sold a number of 'turkeys' in the US (we own an Ilo TV) and I think they no longer exist.