Thank you all for the feedback.

I don't see what could go wrong with a private site. I would modify config.php and replace all refs to the old urls in the database. I guess this should fix also intra-site stuff within a public site. If I am overlooking something serious, please let me know :)

Concerning public sites, I understand this will cause problems, but what would be the difference between upgrading the site as above and creating a completely new instance as @lnxw48 suggests? In both cases, other sites will ping back the old domain and find no answer.

I am considering what responsabilities are implied by making a gnusocial instance public. Closing it or changing its domain name are some of potential issues that came to my mind.