Yes, but not for the first link from the operator in the wilderness to the first digipeater or i-gate. You do not need a data-plan, pay no roaming charges, etc.
As you will have noticed, I tried to take away the tension my initial question seems to have created, and I hope we can leave it with that.
Note that besides the “purists” aspect of my question, there are practical reasons to avoid a data- or SMS-based self-spotting: In the Alps, in particular at the Austrian/German or Austrian-Italian border, a single summit has often contact to multiple national cell-phone networks, and it can be a pain or a costly experience if your phone randomly connects to a more expensive one. Some providers have flat-fees per day and country, and if your phone happens to connect to two countries, you pay twice (happened to me several times already).
Since the SOTA database is Internet-based, it is clear that the Internet is an essential part of the SOTA game, but that does not render challenging the sense of operating Smartphone and rig side-by-side on the summit inappropriate.