The site is offline when installing the plugin

Chat may have things in it that are different than the regular site viewing as I believe it is more real time access vs being able to cache pages.

Agreed. Planned announced maintenance imho is best like in the days old of dos based dial up bbses. There was an option to to have a system message warning the planned maintenance shutdown was coming and would sign out users at the designated time. In those days it was typically for doing mail packets between networked bbses.