They'd probably go nuts about a time traveller who's not even trying to correct a big fucking fuck up in the timeline.
Well, it's not a fuck-up in the timeline. It's a NEW timeline. There's nothing to correct. NO-THING. The timeline from which Spock Prime came is still there, it's past intact and still going along swimmingly as the 25th century approaches.
I think he'd come clean about himself, then as is insinuated in the movie, throw himself into the task of recreating Vulcan culture and society. Just having everyone know he's Spock from another timeline doesn't affect much.
Of course, how much he could affect the future with his knowledge of the events from his timeline is problematic and the topic of numerous other threads.