Does turning off the "Show notifications" settings for apps improve battery life? I recently found that there is a "Show notifications" settings for individual app in my HTC One X. I have turned it off for some applications like Subway Surfers (which tries to sell me coins in notifications).

Will disabling notifications improve my battery life? How does Android handle if notifications are turned off for a particular app - does it only hide notifications from notification bar or it really does not allow the app to create any notifications in first place (so in this case I presume that it would save battery life)?
Disabling a notification for particular app wont' save battery. Yes it would a little by not ringing and vibrating and also by not making you look at the phone.

Actually notification is handled by OS itself. An app just says that I want this notification to be displayed and OS handles it. In your case those apps are running in background using service and periodically asks the OS to display the notification. Event though you've disabled the notification the service is still running and still requesting the OS to display notification.