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.
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.
