Yes. Most neural net applications separate training and inference so that once the net is in production it doesn't change, though it might be replaced with a new net rather frequently depending on how much the distribution of data it's operating on changes over time.
not an expert on this, but wouldn't what you mention be adaptive control rather than ANN?
To add to that, the backpropagation doesn't have to happen on device - they could, for instance, record statistics from a sampling of the cellphones in use, backprop on a server, then push an update to the weights in the next over the air update. The statistics would potentially be much cheaper than actually training the network.