Yes, if an app is constantly looking for updates and then sending you notifications, it will use more battery and discharge faster. Try doing it the other way around. See what apps are sending you notifications and then go into those apps and change the settings. For example if its your email, change the default setting from every 5 minutes to every hour or manually. Checking once an hour (or not at all) uses a lot less battery than every 5 minutes. Some of the apps have notification options in their settings too. If you don't recognize the name of the app (or looks like an ad), see who makes the app. Then go back and see what else you've purchased from that app developer. Then check the settings for that app and see if you can turn off notifications within that app. (There was one app awhile back that some if us ended up uninstalling because there was no option to turn off the ads/notifications. Just don't remember which one it was though.) You might also want to try turning the sound for the notifications all the way down until you get it sorted out. At least it will be less annoying. Hope that helps.
What NookGardener said.
And other notifications can come from the device operating system. I know that my ISP has issues with 'Noise' in the junction box on my street. My Nook HD+ is hypersensitive to any wifi wobblyness, and I get the 'syncing' notification regularly and frequently when this is happening. Not Nook's fault, and not any app I can switch off unfortunately. Fortunately it passes!
@AlbionRose: yes, it is B&N's fault. I sleep poorly and, like now at 4:45 am, like to read my nook HD+ but no matter how many times I change the settings, the notifications turn back on! I do have the main volume turned off, yet when I turn the nook on I hear the notification sound and sometimes it goes off at random in the night so I must turn the while thing off, so I must wait for reboot to read. I've turned off the notes in settings. I've turned down the notes volume. I've turned off auto updates. I've turned off syncing. NOTHNG BLOODY WORKS!