How does Mr. Hooper's veil benefit him in his role as a clergyman? How do these details suggest the theme of the story?

One way in which Mr. Hooper benefits from the veil is that he can now affect his parishioners to a much greater extent than he ever did before he put it on.  The narrator tells us that, on the day he first wears the veil, his sermon was "marked by the same characteristics of style and manner" as his sermons always were, and yet

there was something, either in the sentiment of the discourse itself, or in the imagination of the auditors, which made it greatly the most powerful effort that they had ever heard from their pastor's lips.

Despite the fact that Mr. Hooper speaks as mildly as usual, this sermon is somehow more persuasive, more poignant than any he has delivered before.  In fact, every listener "felt as if the preacher had crept upon them, behind his awful veil, and discovered their hoarded iniquity of deed or thought."  They feel more understood by him than they ever have; it's as though he somehow knows them more fully, and this feeling makes them extremely uncomfortable because there is something they wish to hide.  Moreover, when he goes to pray over the body of a recently deceased girl,

The people trembled, though they but darkly understood him when he prayed that they, and himself, and all of mortal race, might be ready, as he trusted this young maiden had been, for the dreadful hour that should snatch the veil from their faces.

We begin, now, to understand what this veil represents.  That his audience feels that he, with his veil, has "discovered their hoarded iniquity of deed or thought" and that it is death, alone, that will "snatch the veil" away, helps us to see that the veil must have to with our secret sinful thoughts or actions.  Our pretense -- portraying ourselves to the world as sinless -- separates us from one another, preventing us from truly knowing each other, and will only be lifted when we die.  If the thing we fear most is the revelation of our sinfulness to another person, then we can never realize that we are all sinners (a popular Hawthorne theme), and it is our unnecessary deception that ultimately -- and unnecessarily -- alienates each of us.

Furthermore, if Mr. Hooper were to just come out and accuse each of them of being a secret sinner who purposefully hides their true, sinful, natures, his message would seem a lot less palatable to his listeners. Wearing the veil, however, not only engages them in some critical thinking about why he would wear it and what it represents but also precisely conveys the point that we all do this.  Even the minister hides his true nature, recognizes the universality of the pretense, and STILL doesn't have the nerve to tell them what the veil means.  Therefore, this need to present ourselves as sinless creatures seems to be a real deep-seated human impulse.  Not even the minister can escape it.