While I am not personally persuaded by this claim, I will point out some evidence you might use in order to support it.
On the day he begins to wear the black veil, Mr. Hooper gives a particularly effective sermon regarding the subject of "secret sin, and those sad mysteries which we hide from our nearest and dearest." His parishioners seem to feel that he has "crept upon them, behind his awful veil, and discovered their hoarded iniquity of deed or thought." Thus, it seems possible to interpret this as evidence not only of Mr. Hooper's understanding of and empathy with his congregation but also his own familiarity with secret sin. What sins could he possibly be keeping secret? There's any number of possibilities, one of which is that the maiden whose funeral sermon he delivers later was beloved by him.
In addition, it is notable that Mr. Hooper does begin to wear the veil on the very same day that he must preside over the maiden's funeral. Then, when Mr. Hooper leans over the casket to bid farewell to her, his veil hangs straight down so that she might have been able to see his face, were she still alive. "Could Mr. Hooper be fearful of her glance, that he so hastily caught back the black veil?" One "superstitious old woman" declares that she saw the maiden's corpse "shudder" slightly when the minister's face would have been visible to the young woman. One could argue that Mr. Hooper snatched the veil back over his features, even though the girl could not see his face, because he wears the veil as a result of his sinful love of her. She, alone, could have been aware of this sin, and so perhaps he wishes to keep his face covered so that no one else could discover it.