Adding outdoor power adapter to stickup cam battery

I've had a battery stickup cam (ver 2) for more than a year, that I just finally bought an outdoor power cable for, to avoid having to change batteries every few months. (The camera is actually indoors.) When I plugged it in, the app wanted me to switch the camera to plug-in mode, rather than battery. If I do that, will the battery still work if the A/C power fails (it's on a UPS, so that's unlikely)? If I leave it on battery, will the adapter just keep the battery charged, like the solar cell which can be plugged into the same plug? There seem to have been multiple issues with plug-in stick-up cams over the past couple years, so I would rather keep it on battery if the adapter will keep the battery charged. I don't need the additional features that the plug-in mode would provide. Thanks