Perrin will almost certainly back Rand's play, and with Elayne bringing him as a semi-independant ruler and as the liege lord of Ghealdan and near-consort of Saldaea, his support might be the first stone needed to trigger the avalanche and get everyone else to agree to what Rand wants. Up until now, they're used to taking the Amyrlin Seat seriously, so the fact that she has absolutely no qualifications to even be present at a summit of world leaders will not matter so much as the opposition of her office to Rand. But once someone is willing to be the first to take that step of defying the Amyrlin/White Tower, it might inspire the rest to fall in and support Rand.