Not on LTE protocols. Not using a COTS 4G/5G Phone. Satellite phones aren't in the context of this discussion.
You can just about get SMS emergency coverage with the latest generation of modems and aerials designed for the purpose. NTN standards are a long way off being set.
NTN phones have been available since the early 2010s, some even using geostationary satellites (which are 100 times farther away).
If you mean 5G NTN, I believe the newer Pixel models already use that already, and I've been using it using a dedicated device since Summer 2023. They actually use at least some of the same satellites of the 2010s voice service, which I believe is no longer being offered.
I'm talking specifically the ongoing 3GPP work from Rel-16 to Rel-19, and the proposed work by Qualcomm and Thales to validate the use-cases for formalisation of the standard.
Rel-18, the initial release for 5G-Advanced, only brought in the support for the new frequency bands for NTN above 10 GHz - the Ka band where most of our interest lies for large-scale large-bandwidth provisionment - in June of last year for equipment manufacturers.
You're not wrong in saying that most of what we hope to be achieved with NTN is, to be fair, NTN-NR - or 5G NTN - as a lot of it depends on NR technologies like MIMO and beamforming in certain spectrums.
Skylo did the first rollout of emergency SMS in Europe as per the 3GPP Release 17 specifications for Direct-to-Handset (D2H) connectivity in Q4 of last year. Note that Rel 17 designated only two usable frequency bands in Release 17 for 5G NTN use in the 5G FR1 range
> Skylo did the first rollout of emergency SMS in Europe as per the 3GPP Release 17 specifications for Direct-to-Handset (D2H) connectivity in Q4 of last year.
I've been already using that exact service in Summer 2023 in both the US and Europe (Bullit, via Sklyo and using Echostar/Terrestar satellites, I believe). It's possible that that was using pre-release specifications, though.
For the last 30 years.
And the Starlink satellites are much closer to Earth than the satellites we used to hit back then.