Will updating OS X Server over VNC kill my VNC connection?
VNC is one of the base OS X services, and is not provided by Server.app. You can safely update Server if VNC is the only service you need to connect. I have updated server many times in the past over VNC.

However, if you are using Server's VPN to make a secure connection and are running VNC on top of that, you may have problems. VPN is one of the services provided by Server.app, and it will be turned off when updating Server.