Noticed that running Command 1 (below) does not update comparators next to the furnace so that they output a redstone signal. Running Command 2 (below) on a spot currently occupied by a furnace with items in it's inventory does however update a comparator and causes its output to change to no signal.

Further Clarification: Using /setblock to replace one block entity with another (given that the initial block entity had items in it and caused a comparator to output a signal) will update the comparator adjacent to the block entity, but replacing a block entity that has no inventory items (or a normal block) with a filled one will not update the comparator.

Command 1:

/setblock ~2 ~ ~ furnace 0 replace {Items:[{id:stone,Count:1,Slot:0}]}

Command 2:

/setblock ~2 ~ ~ furnace 0 replace