No it won't, because reproducing works verbatim is basically the definition of overtraining a model. That's a bug, not a feature.

A lot of further progress is going to be made towards making models smaller and more efficient, and part of that is reducing overtraining (together with progress in other directions).

Reproducing Harry Potter is a bug, because it's learning stuff it doesn't need to. So to the contrary, "it's just a matter of time" until this stuff decreases.