I get the following message while trying to share a question from a non-public beta site on Facebook:

Log In - Code Golf - Stack Exchange
http://codegolf.stackexchange.com/q/2/6
Warning: this site is currently in private beta for 6 more days. Unless you committed to its Area 51 site proposal, you won’t be able to log in!

While I am fully aware why this happens, my question is, while sites are non-public should the share links be included at the bottom of a question.

Because they are just about useless if the site is non-public, and a little confusing if you are not familiar with how authentication and the web works.