Hoppers do not pick up items from chests/dropped items if powered indirectly but they take items from hoppers if pointing into hopper. The debug screen (F3) says the enabled = true. for all hoppers..

Setup:

Place 3 hoppers on top of each other
Place a solid block next to the middle hopper
Place a Redstone torch on top of the block
F3 screen says enabled on all three hoppers.
Drop item on top of top hopper, it is left to bounce
Place chest on top of top hopper, item left in chest
Place hopper facing into top hopper from above and the item goes through all hoppers

Same result happens if instead of a torch next to the top hopper you have a piece of redstone going into the block. So have two blocks going out and 1 below of the first block. Remove the torch. Then place dust on the block 2 away from hoppers and power it through a torch, lever etc. Same result

Edit: The hopper locks if the redstone dust is going into a block below the hopper but not if it going into a block next to the hopper

Edit 2: Seems to be that the hopper must be updated to change states between enabled/disabled when indirectly powered in the methods mentioned above. Then when it is unpowered it must be updated again