No. The stars are essentially on a sphere at infinity, so you only get a 2-D pointing (RA,Dec). 3 stars would be enough to solve that, but there are so many stars that a 3-star pattern is not distinctive enough; we use 4 stars to make a more distinctive feature. You can think of a 4-star feature as 2 3-star features that share two of the stars.
From an image of the sky, for navigational purposes I think you only get effectively one (RA,Dec) coordinate; call it the center pointing of your camera. I have never worked out the math of celestial navigation, but I think in short that Dec coordinate, plus/minus the zenith distance (= 1 - altitude = angle down from straight up) gives you your latitude. If the camera is along the meridian line, then RA gives you the Local Sidereal Time, and with that and the UTC time/date you can work out the longitude.
cheers,
--dustin