Insofar as everything is related to monads, yes ;)
In fact you don't need to use monads at all here. I've used this pattern on merely applicative non-monadic initial algebras before; in fact, the article's "arithmetic expressions" example isn't what I would call "monadic", because it doesn't readily admit Bind as currently phrased.
Worse, the "writeSmallOddToFile" example isn't even generic at all, so I don't think there's a reasonable sense in which it could even be said to be functorial.
In fact you don't need to use monads at all here. I've used this pattern on merely applicative non-monadic initial algebras before; in fact, the article's "arithmetic expressions" example isn't what I would call "monadic", because it doesn't readily admit Bind as currently phrased.
Worse, the "writeSmallOddToFile" example isn't even generic at all, so I don't think there's a reasonable sense in which it could even be said to be functorial.