I turn mine off.
But then the boat is trailered all the time. If you decide to turn yours off while it's in the water make sure the bilge pump still works, or you may have to leave the "house" battery on.
Even if your engine is EFI/MPI there should be a sparate hot wire for the computer memory. Turning it off won't have any effect on that.
I wouldn't feel safe going away while it's in the water without a shore powered battery charger and someone to check on it from time to time.
Whatever you decide.