Ouch! I would leave the battery out of the camera, but I am suspecting that it would stress and drain the on-board battery for the clock, and the camera might reset itself. If the setting held and the on-board did not drain the rechargeable one, I could live with just resetting the clock. But, I think that I am going to send it in.Good luck with the repair. Mine caught me out last week though it was my own fault. I used my GX80 trying to replicate a situation that @WaltP reported with the EVF darkening during focus assist magnification. The camera died within a minute or so of use. I forgot about it and then a few days later I took the camera on a 5 mile hike to a very scenic location. I swapped to the spare battery which of course was also completely dead.
I think I got around 3 weeks out of the in camera battery with a little use in between. I'm not so sure about the out of camera battery, I think I last charged it maybe 6-8 weeks ago but I did leave it on the 3rd party charging shoe. This is a habit I'm trying to break, though it was never a problem with my EM10's spare battery.