I use it for most of my apps that I play with during the day to hibernate them when I'm not using them for battery savings, such as Rom Toolbox, Dropbox, Advanced Taskmanager, Playstore, Dolphin, Pure Calendar, etc.
But you probably still know the answer to my question...
Greenify hibernates the app until it is active once you close it then it goes back into hibernation. If you have notifications set to go to your device then you will still get them by email or through facebook messenger if you have it.
Some apps just won't hibernate though. Mostly system apps. I've had some *** backward coded apps constantly wake up after being put down. Greenify has an option to show how many times an app has woken up the device. I use that to decide if its worth keeping.
My messenger (8sms) is great sleeping, so I never do it. Careful with clocks, keyboards. Some don't take kindly to greenify and either break or constantly fight it.