Do users incur any charges for receiving push notifications on iPhones, even if indirectly?
Push notifications will mean charges are incurred if you ever pay for data. Clearly, most push notifications are very small transmissions, but they almost always use data connection instead of WiFi so if you had thousands of pushes, it might be the bit of data that exceeds your quota and racks up more cost. Also when roaming, all data might be metered a la carte, so you would in essence pay for each notification you received while roaming.



As outlined in the comment by Matthieu.

Push notifications are data.  If you are "roaming" (ie. outside the country where you have your service contract with your mobile service provider) you will incur charges.



Having said that there are plans which allow for free data roaming globally.  Such as the T-Mobile plans available in the US. This has something to do with the fact that T-Mobile is Deutsche Telecom.  On such a plan there will be no charges.