I agree with Patrick, Banal and Shea. I can see our clients wanting to edit their websites on mobile though having it as an actual app I don't think is the right approach. It would need to handle the custom features we may have in the CMS plus dealing with a whole different level of device compatibility.
While this custom functionality could be exposed by an API, I still see issues for how someone would even login to the app. You would have to specify the domain, username and password for logging in - so only one extra field here, clients could probably live with that. What if though they have multiple separate sites they manage (I assume they would have to login and logout, could get tedious - a browser could maintain multiple login sessions at once across separate sites) or are using a module like subsites (or multisite)? I can't really imagine something like that being handled by the app in a custom way. Rather than having to modify an API to expose that and have all those extra custom bits in the app itself, use what is already built and accessible in the CMS and make it responsive.
From a maintenance point-of-view, I also don't see the need to also manage a separate codebase for this app when really all you need to do is specify a few extra stylesheets and modify some JS in the CMS (I know that is simplifying the changes required a bit but you get the idea).
To summarise, good idea (CMS editing from mobile) though I don't recommend the "app" approach. :)