Darkrai can't take part anyway, I'm afraid! Event-only Pokémon and main legendaries, as a general rule, can't, and any Pokémon with a banned move or item can't take part at all either.
Banned Pokémon:
Mew / Celebi / Jirachi / Deoxys / Manaphy / Phione / Shaymin / Darkrai / Arceus / Victini / Keldeo / Meloetta / Genesect
Mewtwo / Lugia / Ho-oh / Kyogre / Groudon / Rayquaza / Dialga / Palkia / Giratina / Reshiram / Zekrom / Kyurem
.. and Chatot.
Banned moves: Dark Void, Chatter, Sky Drop
Banned items: Soul Dew