Thinking this through a bit more. It’s the server (eg. Signal) that sends the push notifications to Apple/Google. So turning off notifications on your phone presumably means that that Apple/Google doesn’t send them to your device. However they are presumably still be going from the server to Apple/Google (because how would Signal know that you’ve turned notifications off on your phone)?
I think it means that notifications aren’t sent, but it’s a good question.
Thinking this through a bit more. It’s the server (eg. Signal) that sends the push notifications to Apple/Google. So turning off notifications on your phone presumably means that that Apple/Google doesn’t send them to your device. However they are presumably still be going from the server to Apple/Google (because how would Signal know that you’ve turned notifications off on your phone)?