Preview at WWDC likely in June, followed by September launch.
New Dropbox SDK Satisfies App Store Review Guidelines
Dropbox has continued to tweak its SDK in order to fully comply with Apple's requirements, and while Apple has not officially given the latest SDK its blessing, it appears to be satisfying App Store reviewers.
So we didn't get an official verdict (imagine the worst game of telephone you've ever played), but we do have reason to believe that this build is more likely to get approved than the previous build I posted earlier. [...]Filip Radelic, the developer behind Cambox, quickly incorporated the new SDK into his app and submitted it to Apple yesterday. The app was quickly approved by Apple's reviewers and it is now available in the App Store.
What has changed is if the Dropbox app is not installed, it opens a login view directly in your app rather than going to Safari, and there is no option to create an account.
Cambox's settings page with Dropbox options and login webview
Dropbox notes that the new SDK does not allow for account creation through the login webview if the Dropbox app is not installed on the user's device, but the company is hopeful that it will be able to add that feature as it continues to work with Apple to ensure the SDK's compliance.