Question:
During HA Sync, does the old/stale default route get removed from Secondar Node?

Answer:

Any old/stale default route already present on the Secondary HA node will not be removed after HA sync.

During HA sync, the config from the primary is pulled by the secondary. The secondary runs a clear config to clear existing configuration and load the new configuration pulled from the primary node.
 
However, the clear configuration does NOT clear the default route by design.
 
Please see below the man page for the command:
 
NAME
       clear ns config
 
SYNOPSIS
       clear ns config [-force] <level> [-RBAconfig ( YES | NO )]
 
DESCRIPTION
       Clears the NetScaler running configurations based on different levels.
 
ARGUMENTS
       force
              Configurations will be cleared without prompting for
              confirmation.
 
       level
              Types of configurations to be cleared.
              * basic: Clears all configurations except the following:
                - NSIP, default route (gateway), MIPs, and SNIPs
                - Network settings (DG, VLAN, RHI and DNS settings)
                - Cluster settings
                - HA node definitions
                - Feature and mode settings
                - nsroot password
              * extended: Clears the same configurations as the 'basic'
              option. In addition, it clears the nsroot password and feature
              and mode settings.
              * full: Clears all configurations except NSIP, default route,
              and interface settings.
              Note: When you clear the configurations through the cluster IP
              address, by specifying the level as 'full', the cluster is
              deleted and all cluster nodes become standalone appliances. The
              'basic' and 'extended' levels are propagated to the cluster
              nodes.
              This is a mandatory argument.
              Possible values: basic, extended, full
 
None of the levels of clearing will remove the default route from the configuration.
As a result, any default routes present on the secondary node when HA sync is performed will not be removed.

However, the other static routes configured will be synchronized as expected.