Yes connectors that support incremental replication will output state after running successfully, meltano stores it for you, then on the next run it retrieves it and passes it to the connector. See
https://docs.meltano.com/guide/production#storing-metadata for a bit more info, meltano uses a local sqlite database for this by default so depending on how you deploy airflow you might need to configure a remote database for this or a an alternative
state backend so state is presisted. Theres also the
state cli command for interfacing with this stored state if you ever need to check it, change it, delete it, etc