Well, it really depends.
Most Orthodox I’ve talked to would love to see an increase in the Western Rite, and a re-establishment of Western Orthodoxy throughout Europe. They would love to see the Western Patriarch re-established. This fantasy future doesn’t, however, usually involve reunion with Rome. Most I’ve talked to don’t take reunion as a serious possibility. They would support, however, in this (rather bizarre) scenario, the new Roman Pope adopting Western Orthodox practices (but I rather doubt that’d be the Novus Ordo. No Orthodox I’ve yet accept the Novus Ordo as an acceptable Orthodox Liturgy).
Yet there are also those who don’t accept Western Orthodoxy and would encourage this new Western Patriarch to adopt the “tried and true” Eastern practices. The Greeks are rather well known for this position, and are the friendliest with Rome and, of course, His All Holiness is the most likely to be this new Eastern Western Patriarch. So there’s a wrench there.
Really I could go on and on. There’s a million different ways this scenario could be played out, and I’ve only touched on the Ortho-centric ones.