[suddensleep]

My intuition says yes; if a wrong number is placed in a square and then taken as ground truth for solving the rest of the puzzle, it certainly seems like the error would propagate.

As a concrete example, say you misplace a '2' somewhere within a given puzzle. Obviously, this cell is incorrect. But depending on the nature of what the NN has learned, it may believe the row (resp. column, 3x3 box constraint) already has the '2' in it, so tries to fill its correct spot with another number. Which of course then leads to the column and/or 3x3 box of that cell to learn an incorrect value, starting the process over again.

This same phenomenon can be seen in the game Kenken; depending on the strategies you use at any given point in the game, one mistake can propagate outward pretty quickly and spoil large sections of the puzzle.