I've been attempting to measure whether the solar panels are charging the battery or not. I have full sun on them around noon and am monitoring the 12-volt battery at around 12.62 volts on my digital voltmeter. Covering the panels doesn't change the voltage at all, even after waiting several minutes. Uncovering the panels again likewise does nothing. There should be at least a small change in voltage if the panel is charging the battery.
I also measured current directly. I never saw any reverse flow of current into the battery. In its quiescent state, the car seems to draw on the order of 20 milliamps from the 12-volt, probably to run the clock, keep the nav system memory, probe for the intellikey, etc. It's a very low draw, and it would take months to deplete the battery. Again, covering and uncovering the solar panel made no difference that I could detect even at this low current.
Opening a door and running the interior lights draws about 4 amps(!), then closing it again, the system continues to draw 1.5 amps for a few minutes, dropping to a lower level later on. I suspect that waking the system leaves it in a more alert state, running some computer or probing continuously for the key; who knows? My thought was that if the battery were fully charged to the point where the panel wasn't putting current in, then discharging the battery a bit for a few minutes should make a difference. It didn't seem to.
The upshot is that I can find no evidence that the solar panel is even connected to the 12-volt system, leaving a big mystery as to its purpose, beyond the obvious marketing gimmick.
P.S. I read somewhere -- in the manual? -- that the Leaf wakes itself up every week or two to recharge the 12-volt battery from the traction battery using its DC-DC converter, just to make sure it doesn't go dead. The solar panel is really not needed, even for keeping a charge on the lead-acid battery in other words.