Yes. The Tarbell will contain all the dependencies your app needs.
As for building, when your app depends on other habitat packages, it checks to see if the pkg is already installed locally otherwise it will attempt to reach out to your Depot to get this dependency.
One thing to note is that in one studio session, every time you build a plan, it installs itself into the
So if all you had were plans and no access to a Depot, you would be building your dependency every time to get your app built.
So in the end, get access to a Depot. But no access to depot is required when deploying to your hosts.