Yes, as you're utilizing an SSO which does not implement remember me as it uses session based, cookie SSO, you will not be able to take advantage of Push Notifications.

Push notifications are quite complex, but from the software side if you are logged in and have ticked 'remember me' the service worker will run in the background pushing notifications to your browser.

Now, your browser may ignore them if you haven't given the site permission to receive them. Likewise, your OS may ignore them if you have notifications off for the browser, or you are in do not disturb or in a silenced mode.