I've never received any emails from Sony apart from ones sent from PSN purchases, despite having checked my settings and seeing that it was checked that I was signed up to receive them.
A week ago I finally decided to try unchecking it and the checking it again, updating the status and received an email asking me to verify my email. After I verified it, I received a Sony email about Mass Effect: Andromeda that very day.
Haven't seen any emails about the flash sale or my stats, with or without coupon, though, so I don't know how much that helped, but at least I finally got some kind of email from Sony.