I don't know what the SMS service part of Pushover uses as we don't send SMS through Pushover. The part we use, the main feature, sends a notification through an app the user installs on their device. All of us who receive push notifications through our system have the Pushover app on our phones, some also have it on their tablets and computers.
I like the Apple Watch integration as I can interact with urgent notifications just on my watch without my phone handy.