I tried Drobbox now, and I specifically tested it with a 36MB File not downloaded in Dropbox app (i.e. it has the cloud symbol next to the filename).
You can clearly see how the file is first downloaded, and only after finishing it is ready and the file is readable and usable. Therefore Dropbox works just fine.
What I do not know: Who downloads the file, Dropbox or UIDocumentPickerViewController?
Topic:
App & System Services
SubTopic:
Core OS
Tags: