This is not only possible, it's already a thing with unmodified hardware. The 900 MHz band is a ham radio band in the US, but it's used for GSM in Europe. That

This is not only possible, it's already a thing with unmodified hardware. The 900 MHz band is a ham radio band in the US, but it's used for GSM in Europe. That means that you can quite legitimately set up a GSM base station in the US if you have a ham license, as long as you abide by ham radio regulations (which might require some hacks), e.g. you can't turn on encryption and you need to broadcast your callsign periodically. Then most multiband phones will connect to it thinking it's a European GSM network. I can't find it right now, but I watched a talk where someone described doing just that. 900MHz is also used for LTE in Europe, so I'm pretty sure you could do the same thing with 4G/LTE.