The AGPL licence and requirement for contributor licensing agreements means they can prevent people from making closed-source extensions (like for example if you wanted to tie it into your own internal authentication system), UNLESS you are willing to pay them to license it to you under a dual license.
Can they do that? The "Limitations on Diaspora, Inc." section of the contributor agreement says:
> Diaspora, Inc. will not distribute your Contribution to any third party under any license without also requiring that third party to also make your Contribution available to the public under the same license.
I'm not sure but it sounds like that might prevent them from closed-source dual-licensing arrangements. I suppose that doesn't preclude them from building their own proprietary extensions to the Diaspora software for their own hosted services, although the agreement also states:
> Diaspora, Inc. will distribute the Diaspora™ Software, as a whole, under version 3 or later of the AGPL.
If extensions are considered part of the software "as a whole" then they might not even be able to do that.