The first question is do you need/want a fan? If you need a fan, you need a fan.

BTW, that pendant will not provide enough lumens to help with cleanup. Edison bulbs are great for ambience, but not so much for task lighting, because they become blinding at anything but a very low level. So if you have enough light, taking into account that your body is going to cast a shadow by being between the sink and the central fixture, go ahead. It's a very pretty pendant. But if you need more than decorative lighting, maybe not so much.