Do henchmen/hero's affect the drops that a chest will give? I have seen a lot of controversy over this question lately, and I would like a flat "yes" or "no."
you cant have a flat yes or no. it depends on the chest. for all chest that require a key, they dont effect it. for all treasures(unlocked chests in elona) they dont effect it. For unlocked rewards chests(killroy stoneskin/Fow/UW) they do affect the drops you get.
If you're referring to regular chests that require a key then no, henchmen don't matter at all. They do prevent you from receiving items when opening those infrequent unlocked chests, like the ones encountered in the quests "The Charr Patrol" and "The Deserters."