When "Disable Internet Check" is enabled it will keep the wireless network up in the event that your network's Internet connection is lost.
This is useful if you are planning on making a network that will not have Internet connectivity, or would like to keep access to local LAN resources if Internet connectivity ever goes offline.
However, the Internet check is used by the firmware in a mesh environment to determine which path to the internet is a working path in case multiple paths are available. Disabling the check also disables the firmware's ability to detect a path failure.
In practice, this means switches from gateway to repeater mode, repeater mode to gateway mode, lonely/orphan mode, etc won't work. Let's assume a gateway operating perfectly as gateway for days or weeks. Now its connection fails - normally the internet test will detect this and launch repeater mode to receive a working internet connection elsewhere. However, with Internet check disabled, this node would not be able to establish a connection.