I wonder if putting extensive load on the server could drain the battery in enough time before the sun comes up?
I guess it could be possible.
[1] - https://www.pidramble.com/wiki/benchmarks/power-consumption
It has a "144 watt-hour battery" which looks like thats about 38,918.92mAh.
Certainly would take a lot it seems to drain it to 0% before the sun came up.
It depends.
Different types of batteries have different recommended levels of discharge. Acid batteries should not be discharged more than 50%, while lithium batteries can be discharged up to 80-90%. The Blue Ion 2.0 lithium battery is the best one available, as it can be discharged up to 100%.