Such units exist.
http://www.air2water.net/products.html Standard disclaimer -- no affiliation, that's just the first link I found.
Effectively, you're producing distilled water. The AC unit turns water vapor into water.
http://www.ianrpubs.unl.edu/epublic/live/g1493/build/g1493.pdfI would not want to drink the water that comes out of the pipe for the reasons you state, but if it is available and I don't have a ready source of water other than out of a ditch -- I know which one I'm going to drink.
There have been times in my life that I would have been thankful to have a bucket of AC water available.