When you press the Menu button to take you to the configuration options, there is a little battery icon/indicator in the upper right corner, just to the left of the angled arrow. Without power connected, you will see the state of the battery charge. More white to the right indicates more charge. When power is connected, you just get the little lightning bolt indicating that it's powered externally. THAT should always appear when the device has external power.
Intermittent power at the connector/cable of the 6200 itself wouldn't be indicated in the power to your dash cam, so yes, it is still possible.
Connection to your Galaxy won't have an impact on any rebooting issues.
So next time this happens, disconnect power from the device and have a look at the battery indicator.
It could be another issue altogether that is causing the reboots, but I wanted to be sure we didn't have a power issue first, rather than chasing our tails for a wrong reason.