Yes, Download takes stat changes into effect. Because it depends on the current stats.
Download raises either the Attack stat or Special Attack stat by one stage depending on the foe's lowest current defensive stat (i.e. it will raise Special Attack if the foe's current Special Defense is lower than its current Defense stat). If the foe's Defense and Special Defense are equal, the Special Attack stat is increased. During a Double Battle, Download will add the two opposing Pokémon's stats and calculate the lower stat between both.
Hope I helped!