I'd say it depends on your definition of "production ready". The APIs are likely to be stable and well supported, but the current library does suffer some culture clashes, as they're mostly just done with Swift's Objective-C interop. A lot of the APIs are somewhat annoying to approach due to them being designed with Objective-C in mind. Most standard library APIs will be rife with implicit optionals and require extra type checking, especially if you're implementing delegates.

In particular, dealing with Core Data can be a holy mess with Swift because every single property on a Core Data object is dynamic and implicit optionals. Unlike Objective-C, which will happily pretend like nothing has happened (in many cases), Swift will explode quite spectacularly if you try to operate on nil values, and implicit optionals lets that happen without throwing type errors. Either be very careful with marshalling accesses to Core Data objects, or test thoroughly with different data patterns. Last thing you want is your app crashing because someone filled in data in your app that leaves a property set to nil.

I'd expect some resistance (on top of the "I need to learn a new language" part), and some swearing about all these "if let"'s or "I thought Swift meant no more null pointer exceptions!", but it's perfectly doable.