If using the CA-DR1130 hardwire kit, the Kenwood dash cam’s, the batery shouldn’t really go below 12.2V – 12.4V however, Kenwood doesn’t specify the limit, other than simply saying under 12V which of course bizzare and I doubt it would get that low.
The G Sensor accelerometer detects sudden movements, such as a vehicle going at sufficient speed past rocking, high winds and of curse if some try to get in the car or on impacts, so if the car is parked on the drive, there should be very few false alarms.
No amount of voltage protection will prevent the battery degrading, if left for long periods of time and in its best to unplug it.
An OBD or similar solar battery charger connected to pins 4 & 16 (battery power), will keep the battery topped up during the day, as will the small jump start battery packs.
The other option is buy your own dash cam and power it from the OBD11 port (Most reputable leads have battery protection built in)