Peter: White balancing the camera does not improve the low light capability. As the previous poster says, it is basically an illusion that you see a better low light. When you do not white balance the camera specially in theatrical situation the blues, reds and other problematic colors in videos become appear quite noisy and murky. White balancing the camera properly does not imply you are getting a better low light capability.

The color correction in post can do some improvement to the overall picture but remember that the "fix it in post" is not always a good a idea.

Well, the footage has already been shot, so fixing it in post is all I have left.

Anyway, we can argue semantics as to whether "low light" performance is improved, but it seems to me if the picture looks better (i.e. colors are less noisy and murky) then that's all that matters.