First of all, redundant is not bad in UI design. Stuff should be where users might be looking for them, not the other way around. Sometimes you'll have to put an element on several places just to make sure users won't miss it.
Now, to your question. The first rule in Jakon Nielsen's 10 Usability Heuristics is visibility of system status:
The system should always keep users informed about what is going on, through appropriate feedback within reasonable time.
Users should be able to immediately tell if everything's OK, or if there's something wrong.
Cloud storage is still like "black magic" by many many computer users (some are still struggling with understanding local storage). If the service you're offering is of file syncing, and you want users to be sure that their files are synchronized at any given moment, you have to supply some sort of indication that the files are in fact synchronized. Otherwise, users can get easily confused and unsure, asking themselves: are the files synchronized now or not? Remember, you're in the business of back-up. You want to help your users relax and trust you with their files. The small green "V" on files Dropbox has completed syncing re-assures the user everything's fine. You should use some kind of indication as well.
This is very similar to auto-save notifications on web applications, such as Google Docs. "Saved" is the default system status, but because most users of these products have migrated from local storage based desktop applications, they constantly need reassurance that their files are saved (even though they didn't have to manually do it!).
Of course you don't have to use these green ticks like Dropbox. Just make sure that you test whatever metaphor you use on your target users to make sure they create the effect you're looking for.
As cloud storage becomes more and more ubiquitous, and people stop using local storage, this might change.