Regarding backup as and when, I would follow Google's method, simply informing the user that "All changes are saved in Drive.".
However, there is one type of action to which I would add "save", so as to make users more comfortable. I guess the question "Is my document (or: anything else) checked in?" is requested by the user whenever he tends to leave – either when the job is done or when he can not continue working on it at the moment. Thus, if there is a button allowing the user to leave the document ([Quit], [Exit], [Close] or anything that leads to a logically different domain, like [Preview]) I would just like to change the text on for [Save and quit] or [Save and preview] (although it is almost obvious that the job is saved before the preview). I would simply ignore the actions that "divide" the main path – such as printing or exporting – these usually do not affect the main use flow; of course, everything depends on a specific system.
Interestingly, I find it necessary only for people of a certain age, those who remember applications that could work this way – I mean shut down without saving or even asking to save something with changes in progress. I think that people under 30, for example, will need much less than older people. But that's just guessing. We come from vairious points in the techno-cultural space, strongly deformed along his t axis. So everything has to be tested – without that "I can only say what I think users think", as someone has said;)