I guess if you went for the whole "holding a gun to the head brings on the emotional high needed to summon a Persona" thing like they did in the English translation, it could be okay (at least, that's how I interpreted it). You could always assign legendaries to different arcana and get people to choose from them (or even choose for them based on their personality). Stuff like Ho-oh/Cresselia (Sun/Moon) would be obvious, Arceus would be judgement and maybe an ultimate arcana for the group?
Or, if you wanted everyone to be wild cards, have Pokémon types associated with relevant arcana and people can 'catch' them after fighting them. You might have trouble with people wanting to catch the same one, I dunno. Please please please feel free to dismiss any of these ideas as I'm just babbling now...