MON is a global setting that can be enabled at the HCX service level. It doesn't require further action at a per-VM level (Router Location) during the migration process. When you enable MON in HCX, it applies to all VMs that are part of the migration and attached to the NSX segment created after extending the network.

When you change the gateway of an extended network from the on-premises site to the cloud (referred to as "Failover" in disaster recovery scenarios), the routing of traffic will indeed shift to the cloud side, specifically through the Tier-1 (T1) and Tier-0 (T0) routers on the cloud site. This change in routing is a fundamental aspect of disaster recovery and failover processes.

During this failover scenario, Mobility Optimized Networking (MON) may not play a significant role in determining the routing path because the primary goal during disaster recovery is to quickly switch over to the cloud environment and make it the active site for running workloads. MON is primarily designed to optimize the routing path during ongoing migrations, not necessarily for failover scenarios where the cloud site becomes the active site.