Yes, it is best to leave the pedals in the “up” or “flat” position. This leaves the least amount of tension on the strings and on the instrument. For greatest accuracy, you should also be tuning with the pedals in this position, too.
I doubt it would cause the harp any damage to leave them engaged, but it will shorten the life of the strings. Just like with levers on a lever harp, best to leave everything disengaged when not playing.