How do you quickly determine if a client’s license includes something like Experience Analytics? Is it basically that if the license wasn’t good for a component, it wouldn’t show up on the Launchpad or work, or is there somewhere in the license itself to see? I can see Experience Analytics on the CM, and it looks like it's collecting data (I'm not sure it's any good but that's another story), so I'd assume it's licensed but I'd like to be sure.
You can look up installed licenses from the Content Editor. There might be more ways to reach this, but that's where I normally go.
Then check for your specific license. In this case xDB.
Unfortunately I know of no easy way to determine, exactly what license key is required for the various aspects of xDB. But anything not licensed, should not be showing up on the dashboard.