No, you don't. In fact you're not legally required to notify them if your work permit becomes void for any reason. They may fire at that point but in all reality no one checks that deeply and even if they did - USCIS in general doesn't keep track of that stuff until time for renewal comes.

Regarding consular processing the process is that after the interview you are issued an immigrant visa. You become a permanent resident as soon as you re-enter, your visa will be endorsed with a statement that it serves as evidence of permanent resident status for 1 year*. You also have to pay the "immigrant fee" after you receive your immigrant visa, this is solely so USCIS actually prints and mails your green card.

https://my.uscis.gov/uscis-immigrant-fee/

* - The passport with the endorsed immigrant visa can be used in the interim for anything you'd normally use a green card for: I-9, getting a social security card without the restriction text, getting a driver's license, international travel, etc.