By some sort of strange mathematical cosmic entanglement, it appears that  François Brunault answered his own question in the other [thread](https://mathoverflow.net/questions/129143/verifying-the-correctness-of-a-sudoku-solution) while I was writing this question.  

The answer is indeed **yes.**  Feel free to click on the original question and vote up his answer!  Or vote this answer up (I've made it community wiki).