I have a sneaking suspicion that local storage will not quite be so local. Clearly it isn’t local to the camera, in the way that some devices offer. That means, for sure, the sync module has to operate, as you already indicated, but, I’m almost certain, that it’s going to be stored to that local storage by having first been routed through the Blink servers. There are a bunch of things that point to this, but only Blink will know for sure. If I had one, I could soon find out, but I don’t, and I won’t be getting one any time soon, unless I get lucky enough to be given one of the new systems.
If I’m right, it will mean that everything has to operate, just as it did before, and it offers nothing in terms of a fall back solution, which is what many had hoped for/requested in the past, and is what the OP here was looking for with the comment in the third post.