Yep, I have. I've done several tests, and for me it seems to be a rock-solid connection between being able to show toasts from the background and having the notification permission.
Follow-up: At another place in my test app I had a notification. Just to test that I hadn't made a mistake somehow, I removed that notification code.
When I ran the app again, no toast did display, just as before. But when I went into the app settings to enable the notification permissions it said that the app doesn't use notifications, so I couldn't enable it. Bottom line is that I can't make the toasts display now.