On the Prius (doesn't matter the model year), the 12v accessory outlet
(aka cigarette lighter) is switched off when the car is off. So, if
you want to use this battery charger, you'd have to either modify/
rewire the outlet to always be on/hot, or you'd have to wire a 12v
cigarette outlet directly to the 12v accessory battery.
for the power outlet mod:
Such solar cell battery chargers as you describe are used by people
who do not use their car very often, or are planning on leaving their
car undriven for quite a while (such as at an airport parking lot).
There are various parasitic loads on the 12v system, most notably the
alarm or SKS system if installed, that will slowly drain the 12v
battery during extended periods of non-use (besides the natural self-
discharge). The solar charger would keep the 12v battery charged up,
so that you wouldn't need a jumpstart when you return to your car.
When the car is off, the hybrid traction battery is electrically
disconnected from the car. So no solar charger will directly affect
the charge level of the hybrid battery.
Would there be a benefit to fuel economy by using a solar charger?
Well, once the Prius is started the hybrid battery wouldn't have to
recharge the 12v accessory battery as much if the 12v battery is
already recharged by the solar charger (and therefore the gasoline
engine wouldn't have to run so long to recharge the hybrid battery if
needed). But I doubt that you'd see a measureable change in fuel
economy. Mainly, you'd just be able to start your car because you
didn't let the 12v battery get flat in the first place.