In a word, yes. By the series finale of The Vampire Diaries, both Nina Dobrev's Elena and Ian Somerhalder's Damon were human, living a happy, married life.
The series somewhat glossed over the details with more of an "And they lived happily ever after..." approach, but there are a few things that were confirmed, whether in the finale or later in the spinoff shows. Elena became the town doctor, pursuing the path of medicine she always wanted. She and Damon lived a long and happy life together, and had multiple kids: Jenna, Sarah Lillian, and a son, Grayson.
In the spinoff series Legacies season 1, it's also mentioned that they have another daughter named Stephanie, albeit in an alternate timeline.
The first person to get the Cure in The Vampire Diaries was Katherine Pierce, who loved being a vampire and received the Cure against her will.
During a brutal showdown with Katherine, Elena was forced to shove the vampire Cure down Katherine's throat to save herself. The Vampire Diaries season 5 picked up months later, and Katherine was still in Mystic Falls, miserable and ill-equipped to live as a human.
The Vampire Diaries' final season played a little loose with the canon of the vampire Cure, and episode 11, "You Made a Choice to Be Good," introduced new and inconsistent information about the Cure. The rules regarding the Cure in The Vampire Diaries were fluid, depending on what suited the storyline.
Previously, in order to gain the benefits of the Cure from someone who had already taken it, the recipient must drink every drop of their blood. However, The Vampire Diaries' season 8 changed this up, revealing that multiple doses of the Cure could be extracted from Elena's blood, but only one at a time.
In order for someone to be cured of vampirism in the books, all a vampire has to do is smell the rose that holds the Cure. It's a much simpler process but also means it's easier to make a mistake and the wrong vampire smells the rose.
That's exactly what happens in the novels as Damon smells the rose that is meant for Stefan, and ends up cured of his vampirism. Of course, he doesn't remain human but is turned back into a vampire later in the story. That's a drastic difference from the television series in which Damon gets to live out the Cure in The Vampire Diaries alongside Elena.
