As far as the hub goes, you can run it without batteries at all. The batteries are only intended as a short-term back up for if the house power goes out, maybe to last three or four hours. Normally they will not be used as a device should be on corded power.
Also very important for a wellness check system, Very few things in ST can actually run locally at the present time. Right now it’s limited just to a few devices, mostly light switches, and the official “smart lighting” automation feature. And a little bit of smart home monitor. No custom code can run locally. Routines do not run locally. None of the other published smartapps in the marketplace section of the smartthings mobile app can run locally.
So if you did install the “eldercare” smartapp from the marketplace, it’s still not going to run locally.