My estimate is that (at least initially) it won't be actual texting (i.e. SMS) – unmodified LTE and 5G seem way too verbose to be able to handle the constraints of a much higher number of devices per base station, combined with the significantly higher transmission delay and free space path loss.
One of the IoT spinoff standards of LTE and 5G seem much more plausible candidates – they are built with very similar constraints (extremely low received signal strengths, many devices per base station etc.) and are already being successfully used for satellite applications. I've been testing one device using geostationary satellites myself.
But that would require updates to both the baseband firmware and OS of current or future phones (if not entirely new basebands!), and at that point it's going to be very interesting to see whether Apple (accounting for a very large share of the US market) will play along with that or rather push their own (Globalstar-based) satellite solution.