iOS 8 lets us create our own custom keyboards. Is it possible to make a custom keyboard output anything other than unattributed NSStrings?
Can I make a keyboard that outputs images to say the Messages app, or is it impossible?
No, this would be too difficult since most UITextField / UITextView can only handle NSString object.
As described in the UITextDocumentProxy only NSStrings are allowed.
UITextDocumentProxy is the communication object used by UIInputViewController. UIInputViewController seems to be the base for creating custom keyboards.
Also have a look at App Extension Programming Guide - Custom Keyboard