Shared IPs and other environments can work just fine. Many cheaper hosting plans actually share IP addresses, but you should still be able to get SSL certificates for many of those accounts.
The only requirement for the SSL certificate is that your https domain has to be the same as your App Domain, as set in your Facebook application. So, if your website is at
sub.something.com/joomla, you're SSL certificate has to work for
sub.something.com. Some shared hosting plans use a separate shared SSL certificate which displays your something.com site at a whole new URL like
something.sharedhost.com. In that case, Facebook can't establish a verified connection between the two domains, and therefore, it won't use it.
You will need a unique certificate for your domain though, but many SSL certificates can be assigned to the same IP address. If you're host doesn't allow you to have a SSL cert just for your domain, that's a limitation of your host, and will likely prevent the Invite features from working.
Hope that makes sense,
Alex