I did this for the first time a few days ago when I brewed a cream ale, so I don't know if there was a negative effect. I used my tap water and salts for the mash, but didn't have bottled water until my wife got home from the store. I wanted the final salt levels to be what I'd already added so I batch sparged with the distilled. My rationale was that the mash still had salts in the bound water, so I wouldn't leach tannins.
Any experiences or advice concerning this approach? Obviously it would have been safer to blend the tap and distilled for both mash and sparge. I'll report back when I taste this batch.