If a small business wanted to share a common database between all of its employees, is it possible to create a single iCloud account for a specific App rather than for all the iCloud related software on the iOS device?
iOS and OS X only support a single account to access iCloud. It can't be done on a per-app basis.
Furthermore, the iCloud syncing stuff isn't really designed for concurrent multi-user access, it's built for the sort of syncing that needs to happen for personal devices - i.e. that you're using only one device at a time. It's also worth noting that from a developer's standpoint, iCloud is far from perfect, particularly with regards to the Core Data (database schema) syncing and storage.
You don't say exactly what your needs are, but I strongly suspect you'd be better served looking somewhere else for a business-critical app.
I'm not a developer, but I play one --- oh wait, I am a developer. Serioussly, I really agree with CanuckSkier that iCloud is not ready for mainstream user development unfortunately, and that at present, it's not really used in multi-user applications.
I haven't used Google Apps much (I will look at them!), but have been playing with both Dropbox and Parse. Parse (www.parse.com) seems ideal for sharing a multi-user database.
Both Parse and Dropbox have developer forum, have tons of documentation and sample code.
They are terrific to work with too.
Hope this helps..