Pitfalls when updating a site without entering maintenance mode?
As you said there:


  but they have brochureware sites with not a lot of traffic and not a lot of logged-in user sessions (which we do have)


If accessibility is very important to your website I would suggest you do NOT take the risk to directly overwrite files for upgrading while the website is still up and serving. It may lead to corrupt data or broken response. 

One approach could be take one web server out of the load-balance group, upgrade it while your website is still up and serving. After upgrade and test, put it back then upgrade another one, until all are done. In this way you can seamlessly upgrade without shutting down the service. It may sound complicated and boring, but it could be highly automated by writing some scripts I think.