Not exactly.
The existing system is set up as a 2-part integration between your individual blog and the API at WordPress.org. You enter a search term, and your blog retrieves information from WordPress.org. Then you can download themes from the same location. That kind of integration doesn’t exist anywhere else because, well, no one’s bothered to build it.
So even if you could add a tab that pointed somewhere else, you need a somewhere else to point it in the first place.
There’s been discussion on the WP Hackers list and even on this site regarding standardizing an API for hosting your own repositories … but if anyone’s started, their efforts are still in the very early stages.
While there’s not currently a way to add a new tab and browsing to a custom repository (mostly because there aren’t custom repositories), anything is possible.