I am a huge fan of The Vampire Diaries and Nina Dobrev. I believe her leaving will slightly affect the show just because of how long she's been on there and we've got used to her characters. However, it will be as popular as it was without her because the show doesn't focus around her as much as it did in the first few series. If you asked me this question at the start, then I'd most likely say it wouldn't be as popular with her not in it. But times have changed and other interesting characters with amazing story lines have entered and lately, they've been focusing on Stefan and Caroline for a bit too. So to come to a conclusion, the Vampire Diaries will be as popular with or without her in it.
It is my belief that the recent episodes of The Vampire Diaries has prepared the viewers for Nina's exit and in the future, The Vampire Diaries will simply switch their focus to other characters. For example, with Nina Dobrev gone, the show may now focus on the Savatore brothers or Kat Graham and Candice's characters.
The Vampire Diaries' still has many other main characters in which story lines can be created from. Stefan and Damon are still characters on the show, new love interests could arise as well as plot twists. As long as vampires themselves are still relevant, The Vampire Diaries' will still be relevant.
The Vampire Diaries will not be as popular without Nina Dobrev. This is so because Dobrev has a fan base and people do not like to see an original cast member move on or be out of the picture. Dobrev has most male and female followers. They will simply watch something else that she stars in.
One of the most popular storylines on the Vampire Diaries has been the relationship between Elena and Damon. Despite the initial storyline with Stefan, Elena and Damon is the real love story. Without that, many fans are likely to drift away - even though Damon is still there, what will they do with him without Elena? Fans won't accept another relationship for him.