Nope. In GYMs and E4 you can any full team of 6 that can outlevel your opponent greatly. Battle Tower, Battle Frontier, Battle Subway, Pokémon World Tournament and Battle Maison limit the number of Pokémon to 3 in 1v1, 4 in 2v2 and 6 in 3v3 and sets levels down to 50. Number of Legendary Pokemon are also banned from those facilities.