If and how long a thesis parked on a restricted server will be indexed by Google? My thesis has been archived on the repository of my university with restricted access three weeks ago. By "archived" I mean that it has been assigned an identifier online.

So far, however, I found that the item cannot be detected by Google Scholar. When I try to add it in my Google Scholar profile automatically my thesis cannot be found by Google, and when I add it manually in the profile there is no field for me to add the link of the identifier.

I understand that normally it will take from a few days to several weeks to find a new paper and include it in Google. My question is: in my case (thesis archived on the restricted server) if I could find it later until Google indexes my thesis? If yes, how long I should wait for? If not, how can I show an identifier for the thesis item in my Scholar profile?

Thank you very much!
There are several reasons for not showing up in your Scholar profile. Depending on the configuration of your university repository, maybe Google can not access and index the document, just as Ian pointed out. However, even if it is online and available for anyone to see, Google can be blocked (robots.txt) or still have not index those pages. 

So, all you can do is wait for Google to index (without any defined time to do so), or add your thesis to other repository or even to a personal website (if your university allows you to do so).