It's very inconsistent. On a trip I'm in the middle of this weekend, 3 of 4 segments were upgraded at the window and I received an email. the other one was upgraded about 4 hours prior to departure and I received no email.
On a trip earlier this month 2 segments were upgraded at the window, one the morning of the day of departure. No emails.
On a trip around the end of July, 2 of 3 segments were upgraded in advance. Received one email.
I have stopped relying on them. I simply check my reservation myself at T-100, and first thing in the morning on D-1 and day of departure, and about 3-4 hours before departure. IME that's when the 95% of the domestic upgrades will come.
Before the new message format started, the upgrade emails were pretty much 100% reliable.