Thanks for reaching out to the Support Community, and great question! To confirm, yes, there is communication that occurs between Okta verify and Okta.
When devices that host the Okta Verify app are in airplane mode/have no internet connection, Okta verify codes do work to authenticate users who are using another device that does have internet connection. End users have 30 seconds to enter the pass code before the app refreshes with an updated code.
On the other hand, as probably assumed, Okta Verify Push does require a working internet connection in order for the push request to be sent to the device.