I think sturdy would be useful for leads. I'm pretty sure the new rock type learns sr. Focus sash+Lum Berry=ultimate lead.
It could be, but that depends on how the future lead metagame shapes up. As it stands, Skarm, Forretress, Donphan, etc aren't exactly the best leads out there, and Rock/Steel types have a large number of issues aside from their currently-useless Sturdy ability. We'll have to see.
So that he won't be burned, poisoned, paralyzed, frozen or put to sleep by the opponent, which can hinder a baton passer.
I'm sure offensive Vaporeon with Rest/Surf/Ice Beam/HP Electric will dominate on Rain Dance teams, but I wouldn't be surprised if a couple support roles like the one I made up were used, too.
I wouldn't say it will dominate, given the competition. Let's glance at the typical rain team: Lead, 3 Rain Sweepers, 2 Support mons/Rain starters. The best options for Rain sweepers are decidedly Kingdra, Kabutops, and often one of Ludicolo/Omastar/Gorebyss, which means an overload on the water type.
Vaporeon doesn't really add any key resistances to the team that aren't already covered (Water is resisted, lolFire, Steel is resisted, etc), and brings additional Electric and Grass weaknesses. Moreover, it doesn't get +2 speed from Swift Swim, which is what makes MixDra and SDKabutops so deadly, and makes it easily picked off by a powerful attacker.
Vappy may see ocassional use, but it is simply outclassed on a full-blown Rain team. I could see it working as a Vaporeon-Kingdra duo on a balanced team, maybe, but that's it.