Yes. I saw that while in China. I would get push notifications from Gmail and I was able to know what was the mail about without access to Gmail. But, for Facebook I would only get "You got a message". And that was totally unhelpful. Now, I knew that I had a message that I was not able to access too. Seriously infuriating.
https://news.ycombinator.com/item?id=21918595 , https://support.google.com/mail/answer/6603
Of topic, but the ProtonMail service just keeps getting better and better. I just tried Hey email for about 5 days, really liked the pretty UI, but it felt good to switch back to ProtonMail.
I use ProtonMail but most of my email is with people who are on gmail. Oh well.
I know it would be very niche but it would be interesting to see an online store built around Signal, or something similar (assuming a proper privacy policy on not monetizing your data).