No, you do not need this just for decryption. This entitlement is only required if you want your Notification Extension to be able to silently eat the notification. Normally an extension must transform the notification then the system presents it to the user.

APNS is not a "let my server wake up my app in the background whenever and however often I like" mechanism.

Defer handling other things until either your extension or your app would have run anyway and do them at that time.