If you do not have either Jomsocial nor Community Builder installed, but set the "User Profile Integration:" to Community Builder, it will still import the user's email address to the registration form.
Fast forward to testing the form:
I have discovered that if you have an event set to public and have the "User Profile Integration:" set to "Community Builder" (it may happen with Jomsocial as well....I don't know) then try to register for an event as a noon-logged-in user, I get an SQL error. It appears to be trying to import the email address from a non-existent Community Builder profile.
I understand that it would not have any email or other info to import. However, I would expect that in such a case it would simply leave the email field blank on the registration form. I wouldn't NOT expect it to display a SQL error on the public, front page.
I am able to mitigate this by turning off the profile integration. However, it is very nice and convenient to have it import user information automatically. It saves users a step.