No, in the movie "Interstellar," Cooper and Brand would not be the same age when reunited at the end. This is because of the time dilation effects caused by the extreme gravitational forces near the black hole Gargantua, which they encountered during their mission.
According to the story, Cooper enters the black hole and ends up in a higher-dimensional "tesseract" constructed by future beings. From there, he communicates with his daughter, Murph, across different moments in time. He is able to convey crucial information to help humanity find a new habitable planet.
While Cooper is inside the tesseract, time continues to pass in the outside world. The time dilation caused by Gargantua's gravity means that for every hour Cooper spends in the tesseract, several years pass outside. As a result, when Cooper is finally rescued and reunited with Brand, he finds that she has aged significantly more than him. It is implied that many years, possibly decades, have passed for Brand while Cooper experiences only a relatively short amount of time.
The time dilation effects are a central element of the movie's plot and contribute to the emotional impact of the reunion between Cooper and Brand.