There's absolutely no reason an emergency e-call system needs to connect via the car systems such as infotainment. It could be a standalone module that does its own thing regardless of whether the car is permanently disconnected from everywhere. Probably should too, given its nature. And not just could: there are aftermarket e-call systems that do not integrate beyond requiring 12V supply.

This is how cars used to be made. Features were standalone modules: there could be some bus traffic about optional data (wiper module with rain sensor could broadcast that it's raining and body control module could hear that and could be configured to close windows when raining) but they weren't strictly integrated in any meaningful capacity. You could change the radio unit to whatever you liked: if you were lucky you could get one that can actually understand what the other modules in the car were saying and show some non-enterntainment info on its screen as well. Navigation used to be a standalone system that had GPS receiver but nothing else in the car couldn't necessarily tap into the location data.

SUre, it meant some more wires and maybe the features had disconnects because they weren't aware of each other that much but all in all that was a good thing. It kept everything simple, isolated and repairable. Now because of more integration the modules need to know who they're talking to which leads to bizarre things like having to code in new headlights and pair them with other modules or they won't be recognized and just stay off.