We want to open our reunion to other alumni. I want to point them to our site for registration. Can we handle this without setting each person up as a guest? Is there a privacy setting somewhere that would make the reunion planner public?

No, there isn't that option. They need to be added as guests to purchase a ticket. Unless you activate this option below on the Preferences page

CLASSMATE JOIN OPTIONS

You can allow anyone to join your web site or require that only Classmates you have pre-entered on the Classmate Profiles page can join.

X   Allow only classmates I have pre-entered to join site.
O   Allow anyone to join the web site (consider using the New Clasmate Verification Feature below with this option).

The second option would allow ANYONE to join your website, including anyone who happened to find your website.