I was reading up a bit on distilled last night, and it seems the answer to this will depend on who you ask. Someone had said that distilled water is not pure, because any elements in the water that have a equal or lower evoparation point with water will evaporate with the water, therefore staying in it as steam and as it condenses back into water.
However, what I was reading last night claims that doesn't take into account the fact that those elements are frequently heavier than air and water vapor, so will frequently not rise with the steam. Also, most distillation machines run through multiple processes, which also overcome much of this.
Basically, I think the only way to really know for sure is to get a TDS meter. I believe if the TDS (or maybe PPM) is between 0-10, it's considered pure water and PH should become irrelevant (and in fact difficult/impossilbe to measure in many cases).
Then I started reading up on alkalinity and really got lost........