Would it damage the pedal in any way if I recorded a loop, turned the volume all the way down, turned my amp off, and en left the pedal on for, say, overnight?
It's being powered by a dc brick.
Nah, it's digital. It would be more safe to leave it on the whole time than ever turning it on and off.
That said, try recording a loop and and leaving it - the dl-8 degrades a little, really cool especially for ambient atmospheric noise...