She isn't a permanent resident until she's admitted to the USA, where they'll stamp her passport, thereby "endorsing it" and allowing the passport with the stamp and visa to act like her green card for 1 year. I assume you mean you're flying out of the country of Georgia through Amsterdam. While there is travel ban for people who have been in a schengen country within the last 14 days, which would include Netherlands, there is an exception to spouses of citizens and permanent residents, so it sounds like you both should be ok to travel together.
From the text of the executive order https://www.whitehouse.gov/presidential-actions/proclamation-suspension-entry-immigrants-nonimmigrants-certain-additional-persons-pose-risk-transmitting-2019-novel-coronavirus/
"(a) Section 1 of this proclamation shall not apply to:
(i) any lawful permanent resident of the United States;
(ii) any alien who is the spouse of a U.S. citizen or lawful permanent resident;"
They will only send you emails. NVC went paperless couple of years ago. They will only send mail to cases that didn't provide any emails for whatever reason.