What's your front-end? With nginx, I think I'd set it to server the 404 or Under Construction page from a static file. You can also tweak your routes.py to do a similar thing, but the front end will be faster.
The Disable button on /admin/sites didn't seem to do anything on my home setup, W10 with 2.14.6 (yes, I know) and Rocket. So I'm not sure what automatic provisions for site maintenance are supposed to be there.
/dps