All machines have access to the same session state regardless of the "high availability" checkbox.
High-availability checkbox ensures that cache data is not accidentally lost and replicates that data to other servers in the cluster (2nd copy only) - however, even if that wasn't the case, all of your servers have access to cache across all servers.
HA option is helpful only in case of an outage where one of the cache servers were to go down or get auto-scaled down. In such cases, lack of this checkbox can cause issues
HTH