I basically do that - my core database is encrypted on Dropbox and I use a desktop app and web apps for mobile via KeeWeb which is free. KeeWeb on desktop also backs up locally in the event anything ever happens to my dropbox access, but Dropbox is the central sync point. The web app connects to Dropbox and since it's a web app there isn't even a need for the installation of an Android/iOS app. I just keep the webpage up at all times. The app is cached by design and doesn't send external connections.