If your phone is locked you will most likely not get the notifications, it just depends on the app. I do agree it can waste battery. It's important to remember

If your phone is locked you will most likely not get the notifications, it just depends on the app. I do agree it can waste battery. It's important to remember this is only a concern on non-free apps. The FOSS apps have very low power background services that check for notifications without the app running.