From what I've experienced, and what the manual says, the blue light will turn off when the battery drops below 12 volts, even if you have parking mode turned on. This is to prevent the INNOVV from draining your battery too much. If you have a Battery Tender connected to your bike while you're not riding it, it won't drop below 12 volts, so it (the blue LED) would stay on all the time. I think it should shut off at 12.5 volts myself. My Old wing needs good cranking power to start, and 12 volts is at the edge of not enough.
Yes, there will be blue led light on when the battery was above 12 volts.