Ditto to @Michael_Lingelbach 's experience, my HDMI card shows ~900mW draw and for some reason 100% usage on powertop. Possibly interestingly, before plugging in to an external monitor for the first time, the HDMI card if it drew any power was <200 micro-Watts (low enough it did not show in the top ~60 entries in powertop).
Perhaps to someone better versed in the technical details this is a clue to some sort of toggle that may have been tripped during the first HDMI usage that can maybe be un-tripped afterward to save a few joules here and there? Whatever the initial configuration was, it worked fine for recognizing the outputting to the external monitor on first use.