Do applications consume traffic if push notifications are disabled (more in the table of contents)?

Question

iOS

Interested in ios 6.1.3. But if this is true for other ios, then it will also do.
1) If you disable push notifications for applications that regularly connect to the Internet (for example, email clients or instant messengers) in the iphone notification settings, then these applications do not consume Internet traffic in this case, or do they still continue to consume traffic and periodically connect to the Internet?
2) If push notifications are disabled in the settings of the mail.ru mail client application, does the iphone in this case not consume Internet traffic or does it still continue to check mail?

Answer 1

He always checks mail. In ios 9, they added a power saving mode that disables this check (and many others). But I'm not sure about third-party applications.
Push notifications work through their APNS service, the description of which can be found on Habré, or even on Google. This service was created to conserve battery power so as not to keep the entire application running in the background.
And, most likely, the phone with this service keeps a constant connection. And even if you turn off some notifications, you will not greatly reduce the traffic used.