na, will be fine.
It will have been designed for 13.8V because that's the float charge voltage of a 12V lead acid battery
Therefor we can assume it will be fine with a flat 12v lead acid. ~10.5 - 13.8V will be the intended voltage range.
In general a lower voltage doesn't damage things.
An exception is badly built switchmode power supplies that don't auto cut-off at low V and instead try to run with way to much current flowing through the components