The sync behaviour is:
Replies to emails sent from Event Temple will sync
Emails sent directly from your email provider to an ET Contact will not sync
Replies to emails sent from your email provider will not sync
New emails sent from a Contact will not sync
If you send an email from ET from within a Booking, and the guest replies, it will sync to that Booking
If you send an email from elsewhere in ET (i.e not associated to a Booking) and the guest replies, it will not sync to a Booking
It is possible to forward emails from your Email Provider to Event Temple following these steps.
Additional Information