Do the items that increase item drop rate also improve quest loot drop rate?
The answer sadly isn't that clear. Majority isn't affected.
Majority of quest items are defined in text (XML) files, these are under special conditions affected by 2x drop rate and drop rate buffs.
Minority of quest items are defined in scripts (SCP) files, these aren't affected by 2x drop rate and drop rate buffs at all.
The game is designed so poorly, that players can't see any difference which quest is based on what type of file.
Luckily the game version we are currently upgrading to makes many quests easier so players don't have to worry about low quest item drop rates in the first place.