If what is meant by "first-person dramatic" point of view is first person narrator as the viewpoint character, then the answer is yes. John Updike's short story "A & P" is clearly a story that illustrates the sometimes concave view of life that is characteristic of teenagers. There is a protectiveness of perspective that the narrator takes towards the girls since they are of his age group. For instance, when the narrator Sammy first sees the girls, he watches them enter the store:
Walking into the A & P with your straps down, I suppose it's the only kind of face you can have. She held her head so high her neck, coming up out of those white shoulders, looked kind of stretched, but I didn't mind. The longer her neck was, the of more of her there was.
This first person viewpoint character is also evinced at the later in the narrative as Sammy judges the Lengel:
His repeating this struck me as funny, as if it had just occurred to him, and he had been thinking all these years the A& P was a great big dune and he was the head lifeguard. He didn't like my smiling--as I say he doesn't miss much--but he concentrates on giving the girls that sad Sunday-school-superintendent stare.
And, then, at the end, Sammy narrates with yet the girls on his mind,
....but remembering how he made the pretty girl blush makes me so scrunchy inside I punch the No Sale tab and the machine whirs "pee-pul" and the drawer spat out. One advantage to this scene taking place in summer, I can follow this up with a clean exit,....I look around for my girls, but they're gone, of course....and my stomach kind of fell as I felt how hard the world was going to be to me hereafter.
The disinterest that the girls have towards Sammy indicates that his viewpoint is strictly his and the story is told rather dramatically from his convex narration, although he spare himself any criticism.
The short story "A & P" is told in the first person. I have been unable to find any reference to first-person dramatic. "Third-person dramatic" (or "objective") describes an narrator who recounts a story (using he, she, they, etc.) but maintains distance and objectivity. Third-person dramatic cannot move the plot along, but recounts "just the facts."
With this is mind, I cannot see the narrator of the story as "dramatic." Sammy (the boy who tells the story) is emotionally involved in sharing the account of the three girls who visit the store where he works. One of them has such an effect on him that he stands up to his manager at the end when the manager chastises the girls for their manner of dress. (At the time, one didn't walk into a store in a bathing suit. This is still the case in many places today.) Sammy not only stands up to the manager, but he quits his job on the spot.
This is an emotional reaction. The girls are gone: Sammy isn't doing it to impress them. However, he is so overwhelmed by their visit, and perhaps so changed, that he believes quitting is something he must do on principle, even though he reasons at the time that it is probably a mistake. Sammy is intuitive enough to know that after this, things will never be the same for him.
With Sammy's personal involvement, based on the definition of "dramatic" as used with third-person, I do not believe the story is told in first-person dramatic.
(If the term "dramatic" is used to convey a drama or a play, this also would not apply to Updike's short story.)