The short answer is “no” – a built-in laptop camera will work just fine, provided your writing surface isn’t too far away (<10ft or 3m) and your lighting isn’t too dim.
If you’re working in tougher conditions (e.g., bad lighting or small/distant board), consider using a better camera. Full HD (1080p) cameras work quite well, even in difficult conditions. Board contents should still be clear from a distance of around 20ft or 6m.
You can try an even stronger camera (4K) though keep in mind that the higher the resolution, the greater the strain on your computer’s processor or graphics card. Still, if you have a powerful enough system, the higher resolution will definitely deliver a crisper image at a greater distance.