Given Pluto's mean distance of 39 A.U. from the Sun, Pluto receives only about 1500th (1 / 39 squared) as much light per square centimeter as the Earth (with is, by definition, 1 A.U. from the Sun). Nevertheless, the Sun is still much, much more than just a "bright star" as seen from Pluto. In fact, it would outclass every other celestial body in Pluto's sky. Even at aphelion (i.e., when farthest from the Sun, at a distance of 7.3 billion km), the Sun in Pluto's sky is still 150 times brighter than the Earth's full Moon as viewed from the Earth.
As far as the camera on board New Horizons - it is capable of discerning details on the NIGHT-side of Pluto lit only by sunlight reflected from Charon.
Regards,
If Charon is reflective, i.e. white, that amount of light should be significant to show Pluto night side details, given the sensitivity of the detectors this probe is carrying.
You forgot to mention the dozen Sylvania Blue Dot flashbulbs the New Horizons is carrying to use at the fly by. Of course not many people know this. :)