I'm testing this hypothesis. I have not logged into Facebook for three months and am still getting daily emails with links to posts
I can't remember how to login to my FB account (and just don't care to try), so I just set up a spam filter to catch them and delete them. Within the first two months after I stopped logging in, I would receive 20+ e-mails a day from "friends I missed" or whatever. Now it's "only" about 3-5 a week according to spam.