Yes, that's basically the point. You get 'free' continuous learning just by throwing the new data into the pool. Needing an explicit training step is a weakness that makes CL hard to make work for many other approaches.

For any practical application KNN will need some kind of accelerated search structure (eg Kd-tree for < ~7 dimensions) which then requires support for dynamic insertions. But this is an engineering problem, not a data science problem, it works and is practical. For example this has been used by the top systems in Robocode for 15+ years at this point, it's just academia that doesn't find this approach novel enough to bother pursuing.