Nope. QNH reflects pressure, not density
However, do you think a parcel of less dense air will remain stationary in the atmosphere? If you agree that it will rise, then the local surface pressure will fall.
edit: Density Altitude Calculator - English/Metric
It's interesting to note that, "Calculations using dew-point are often more accurate than those using relative humidity because the dew point is fairly constant for a given air mass and changes very little until another air mass arrives, while the relative humidity varies greatly as the ambient temperature changes."
& "The ICAO International Standard Atmosphere standard conditions for zero density altitude are 0 meters (0 feet) altitude, 15 deg C (59 deg F) air temp, 1013.25 mb (29.921 in Hg) pressure and 0 % relative humidity (no water vapor in the air). "