While I had the blower of my 10 year old updraft Rheem 90 HVAC system removed for inspection and cleaning, I noticed that above the fan in the duct there is a coil with black, gooey, fibrous material coating it on the bottom, which sloughs off easily. Is this an accumulation if dirt that should be removed, or some kind of sealer or sound damper that should stay?

That coil could be the air conditioner A coil. If it is dirty clean it carefully.