Синхронизация влияет только на внутреннее время приложения Google Authenticator и не отражается на настройках даты и времени устройства.
Time zones don't matter for Google Authenticator because it is using the Unix timestamp internally...
The only thing that could happen with time zones is that the time zone setting on the server/phone is not set correctly and therefore the machine cannot calculate the right UTC time and therefore the Unix timestamp would be wrong on one machine.