Updating servers at once in web cluster

Question

We have a pretty basic load balancing setup with 3 web servers behind a load balancer connected to the same db server and pointing their wp-content/uploads folder to an nfs share.

We have the first server rsynching the wordpress files across the other 2 in a cron job to keep the servers in sync (all wp-admin stuff is done on the first server)

I'm wondering what the best way is to upgrade the entire cluster at once with minimal downtime. If I update wordpress on the first server, will the db versioning cause the other 2 servers to stop working? Or can I just update the first server then rsync the files across without any downtime?