You know that affect means to have an effect on something right?

The noun sense does not.

affect

noun

    Psychology.,  feeling or emotion.

    Psychiatry.,  an expressed or observed emotional response.

    Restricted, flat, or blunted affect may be a symptom of mental illness, especially schizophrenia.

    Obsolete.,  affection; passion; sensation; inclination; inward disposition or feeling.

Now let's replace that in my original phrase:

> prose intending to imitate the affect of poorly composed sentences

becomes

> prose intending to imitate the feeling or emotion of poorly composed sentences

My point was that the author is trying to convey a specific feeling by way of poorly composed sentences. Perhaps they want a colloquial feel or a ranting feel or a rambling one. An obvious example would be the massive run-on sentence in Ulysses.

Poorly constructed sentences cannot have an affect.

Written text can absolutely signify an affect, and poorly constructed sentences regularly do.