That's a good question. There's obviously more stars in the directions of the galactic plane (what we observe as the Milky Way), but the individual stars that we see in the night sky tend to only be the ones that are really close to us (relatively speaking). So it's a question of which effect dominates the other. I think it'd be interesting to see how well the distribution of stars fits a Poisson distribution.

Well no, if you look at the whole sky then obviously you'd see more stars in the direction of the galactic centre (the milky way) than in the opposite direction, but if you consider only a small sliver of sky the results would be pretty close to being truly random.