When we think "hovering downwind", what we are really doing is hovering in a reduced/zero airspeed state (compared to hovering upwind).
Less airspeed means higher AOA for the same lift, so more drag, more HPR, which equals more torque which equals more T/R thrust which also takes more power.
A helicopter hovering (at zero groundspeed) with a 8-KT direct tailwind may well take less power to hover then the same situation and direct headwind. This because the M/R vortex will be blown away from the T/R. Of course, if the pilot is making significant pedal inputs to hold heading, any such gains will likely be negated.