The short answer, no, you do not need to draw fanart to be popular. I'm not sure if you're aware of them but please look at Yuumei, QinnyArt, RossDraws, Laovaan, and/or Loish.
Yuumei, Qinny, and Loish strictly do original art (I mean, I've never seen fanart from them. They may have done fanart in the past but probably not in the last ten years). I know that Ross and Laovaan have done at least once recently.
Again, the point is, no, you don't have to but keep in mind, these artists have good foundations in their art skills. Yuumei and Qinny's (recently, though I don't think that is what she would normally do given a choice) art tend to be very emotionally charged, too.
No one is going to deny fanart can help get you started but in my experience, it doesn't seem to keep a good loyal fanbase so my advice is to keep doing what you love, never stop improving, and hopefully, maybe one day you'll have something you're happy with. 