It should work, but some networks are really bad at delivering messages, dropping them or delaying them by hours.
As for charges, that may be a problem. But I have never seen international charges of over a dollar for a simple text. But I haven't been to really exotic locations.
I still use SMS for the second factor, it's way less secure, but I have it mostly to protect against opportunistic attacks, and having the second factor bound to a device that I will lose or kill with 100% certainty isn't a great solution for me.
As for charges, that may be a problem. But I have never seen international charges of over a dollar for a simple text. But I haven't been to really exotic locations.
I still use SMS for the second factor, it's way less secure, but I have it mostly to protect against opportunistic attacks, and having the second factor bound to a device that I will lose or kill with 100% certainty isn't a great solution for me.