Can I turn off all "Notification" of all apps, services in Android phone?

I found tips to improve battery in this link: http://www.gottabemobile.com/2012/10/30/hurricane-sandy-crisis-map-puts-shelters-storm-info-alerts-power-outages-on-mobile/ In this link - author said we can turn off Notification of android/iOS applications to save battery. I have an Android phone. If I go to Settings/ Personalization / Manage Notifications (Sony Xperia). I will see all Applications/ Android Services that I can turn off notifications **My questions is CAN I turn off all application notifications (downloaded / built-in apps) / android service notifications (app services/built-in services)?** If I turn off all of them - Does this affect operation of the phone? I understand that I will not receive any notifications (news/updates ... ) if I turn off notifications. I can check updates manually. Thank you!