Nimbostratus
MVPf5learning9 GTM isn't my best area of expertise but from my understanding the sync-group is used to syncronise the DNS configuration between all the GTMs so that each can respond with the appropriate DNS query. From my understaning the statistics each GTM has is unique to the device so I don't believe those statistics would be synced across all the devices. Now if you want to know which GTM is responding to a particular DNS query you can perform a dig +trace which should tell you which GTM responded to your query. Now I don't believe it's turned on by default but I believe you can use the following document to log all DNS queries so you know which client received a response and from which GTM.