This is a question I get asked a lot by those starting to learn to draw. Holding a pencil for drawing is similar in a way to holding a pen for handwriting in that there are ways that get better results, however it is a personal choice. Just like handwriting we all have a unique style so I think the best advice is however it feels best.
This question isn’t particularly easy to answer with a yes or no. Of course you can paint before you can draw. I think the question should be whether or not you want to and not to see drawing and painting as separate activities.
Regardless of if you are drawing or painting you will still be facing similar challenges in creating artwork. Perspective, tone, line, capturing movement, gesture, proportion and composition are all key skills that are going to be challenges in drawing and painting.