A reason this would be helpful/beneficial? A simple scenario would provide other individuals, myself included, a reason to vote for this idea. At the moment, I cannot think of why you'd want to take pictures of an individual on their personal device.
Most likely not going to happen. This would require the application to know about the other applications installed on the users phone. Access to the phone outside of the application can be prevented, rendering this implementation useless.
This would be useless against apps that let you "fake" or "spoof" your location. Just search "Fake GPS location" on Google Play. The iPhone is a little harder if you try to use an app, but you can fake your location with the Web Browsers and TSheets has the web interface that would allow users to clock in using the fake location.
I just don't see this as a feasible approach. What if the person's phone dies but they are still working, should they be automatically clocked out then? How about hitting dead zones? Application permissions on phones, even reporting statistics such as Airplane Mode, Battery Level, are not something that is easily allowed. It also violates certain privacy rights of the phone owner, unless it is a company phone. If you don't trust your employees, and I know there are many who like to abuse the system, then maybe explain to them that if the tracking isn't turned on, they can come to the office building, use TSheets Kiosk (if you have one) to clock in. Obviously the implementation of TSheets was to make digital time tracking more convenient, but if your employees were going to lie over digital measures, they'll find other ways to lie no matter the implementation. Heck, there are a number of apps already on the market that allow you to spoof your location.
Caching the user information, logins and pictures (if enabled), in my experience, should be easy enough to do in the event of a power outage or as another user states, remote location. The tablets will continue to operate on their own battery. Once power is back on and/or the device is reconnected for data to be transmitted, syncing all cached information, as well as verifying any changes, would be great for the Kiosk mode.