If your client has to work when the database isn't available anyways, then isn't that an even stronger argument for a CP database?
If your client is available even in this case, then you have some kind of eventual consistency.
Exactly what I was trying to get at, thanks. The line between client state, server state and db state is a thin illusion. As REST makes explicit, every client operates on a representation of some server resources, which means CAP can come into play in even the most trivial online apps.