No.
Source: I use Drought Nintales and Chlorophyll Venusaur in OU.
In Generation V OU, yes.
Weather + Speed Ability Clause - Teams are not permitted to include Pokémon with the abilities Drought and Drizzle with Pokémon with the abilities Chlorophyll and Swift Swim. They may enter a battle with one or the other.
BW OverUsed (Smogon)
