The display does not normally turn off, just the backlight. If you unplug the mpguino, then it will turn off, but the tank information (miles driven, gallons used) will be erased. I believe the calibration information will still be there, but I'm not positive.
The power that it uses when the backlight is off is very little, I left my car off with the mpguino plugged in for about a week and a half in the middle of winter, and it started up just fine when I got back to it. There have been
reports of people having their battery drained from leaving it sitting for a long time, so I guess it depends on the condition of your battery. Mine is pretty new, so I'm sure that helped. If you're worried about it, the safe thing to do would be to unplug it.