I don't know about this actually. Remember the joint shinobi army doesn't just have the 5 kages, it also has the likes of Kakashi, Guy, numerous other Konoha jounin etc etc. They also have Naruto, who is probably an equal match for any of the shichibukai, except for maybe Kuma and Doflamingo. They also have Killer Bee.
I think the big factor in this fight would be Naruto. He's shown that he can create multiple clones, each of which have power comparable to, or exceeding, that of the Kage. It could effectively be 100s of Kage level ninja vs the Shichibukai, in which case I say the allied army would win. If the Shichibukai can somehow kill Naruto early, then I think the Shichibukai would take this.