What happens after FAD is current if you alreayd have FTA1 before PD

Fellas,

My priority date still isn’t current, but I already have an FTA-1. My case went to a non-local field office and then got transferred back to NBC. Emma also confirmed the interview was waived.

Does that mean they already reviewed/processed everything at the FO and just sent it back to NBC to wait for the PD to become current? If so, once my date is current, should I expect a faster green card approval instead of the usual months-long wait?

Has anyone had a similar experience where things moved quickly after the PD became current in this situation?

Thanks.