You can distribute Mac apps without the Mac Store. However, if your application wants to use iCloud, you need to distribute it through the Mac App Store (or deliver the AdHoc distribution to Mac computers registered on your computer, limited to 100 development machines per year). Only applications downloaded through the Mac App Store can access their iCloud container.
Also: you need to be a registered Mac App developer and sign your application if you want the gatekeeper to automatically open your application (starting with Mountain Lion 10.8.). Otherwise, users need to disable the gatekeeper, change its settings or (first) launch the application through the context menu> open.
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