The option for users to access your Quality Center system across the internet has little to do with the Quality Center application and everything to do with your company's security policies. Your company would have to open up their firewalls to allow access to that internal system from internet IPs. The users accessing the application across the internet would have to adhere to the same client prerequisites your internal users must meet.
Trudy is right on that one. Our facility provides acess to QC via Citrix launched through our external web portal. All users requiring QC access must be authenticated via AD (must have access to our intranet). We can't attach/store documents via Citrix, or report against the database, but all other functions are available.