Yes, your site is very secure. What this means is that your site is actually located on a server that is in a protected building. No one gets in without belonging there. Any visitors must have proper picture ID. Everyone is let in by a guard and a guard is on duty 24 hours a day and 7 days a week. And in keeping with a high state of alertness, everyone must pass through a metal detector.
Plus, the servers are located in a special room that is locked and protected with security devices. It is air conditioned and there is a diesel powered backup in case there is a local power supply problem. And in case of a catastrophic natural event, the data is backed up at another location. Both of these data centers are connected via fiber optics to the main internet backbones so there is redundancy in network access at the greatest speed possible. Security of our servers is a very high priority.
As for intruders via the internet, your site is like an unlisted phone number. Yes, it is true that people can accidentally dial an unlisted number just as they can accidentally get into your website. But without the password, they can't join your chat room. And if you want, you can have all of your pages password protected. You give the password to anyone you want and can change it as frequently as you like.