Connecting an external network using domain mapping plugin?

My question is regarding the domain mapping plugin. I don’t think I am completely clear on its purpose.

If I am setting up an EduBlogs Pro type of arrangement where all sites are hosted on the main domain, like; Would domain mapping only give you the option of having your own custom domain name while still being forced to remain within the Edublogs framework? So even if I had my own domain, there would be links at the top navigation which would link back to the main type of site?

Would this mean that if I have a client that wants more control over their branding etc, it would be better to start off building their network on their own domain, rather than on the main Edublogs type of framework?

And if I did it this way, is there a plugin available which would ‘connect’ their site with the other main network? Could I set it up so that some users who are logged in at the client’s branded site can automatically be logged into the main type of site?

If this is the case, the last thing I need to figure out is whether the WP-multi networks plugin will allow me to keep everything all on one main network. But I am not sure what the advantage to that would be. I might as well just put such clients on their own domain with their own Cpanel etc.