Can acid mine drainage form acid rain?
I don't think acid rain formation from liquid acid mine drainage is very likely.  The reason is that in acid rock drainage (a.k.a. acid mine drainage or AMD), the acidity is caused by sulfuric acid.  Sulfuric acid, $\ce{H2SO4}$ is much less volatile than water.  It simply won't appreciably evaporate from bulk liquids at normal conditions on the Earth.

There is one condition where acid mine drainage could possibly contribute to the formation of acid rain: if there were lots of aerosols formed from acid mine drainage waters.  If there were an AMD-laden stream or creek that flowed over a waterfall or was otherwise agitated enough to form very small droplets and splashes, some sulfuric acid might travel to the atmosphere in the small aerosol droplets.  That could contribute to acid rain, although a more likely effect would be a much more local (tens to hundreds of feet) acidification of the environment.

However, even then, I suspect that sulfur from coal combustion would be the dominant source of airborne sulfuric acid in most regions.  In the United States, coal consumption is roughly one gigaton per year, leading to about 20 megatons of sulfur emissions to the atmosphere.