Yes. (at least on iOS, not sure about Android or Win)
Parse has an iOS data object that syncs properly, whereas there is no evidence that any developer has ever gotten Apple's own iCloud + Core Data to sync properly at the record level.
Parse is cross platform so you can easily get the same data for a user on a desktop, web, android, iOS and windows mobile app.
Cobbling all this together with Heroku + libs would be possible but would require a lot of work. Parse just works out of the box.