I'd hope the system would allow users to have their own dependency dbs layered on top of the system's. That way I could add (say) TenGen's MongoDB or Caffeine to my apt sources without affecting everyone on the system.
Packages would probably have to have some sort of indication that user-installable or not. It doesn't make sense to install the kernel into your home directory. Probably x.org too.
It might get weird if the user does a dist-upgrade before the machine admin. Or, if your idea of local installs automatically converting to system-wide ones works, then maybe everything just works.