Correct. It has nothing to do with your phone. The system is independent, once set-up and running. Wouldn’t be much good if it all stopped working just because your phone battery went flat, was out of signal area, or indeed, was in airplane mode.
Of course, in any of those statuses you can’t view the clips, but they are still up there in the cloud, waiting for you to access them once more, with a functional device, when you can.