As a natural beauty care business...I say yes. Fair skinned people need to focus on their lips. That's where they will give the most impact without looking too 'made over'
Does black eye shadow/black smokey eyes look too harsh on fair skin?
No. I'm incredibly pale and love a dramatic smoky eye. As long as you make sure to blend the edges out thoroughly you can rock it. Make sure to take a clean blending brush when doing this so you don't just just smudge it.
I'd also recommend blending a warm transitional colour between the smoky eye and the highlight on the brow. For example, a brown or pinky taupe. This will held tie the look together and make it seamless.
I wouldn't recommend wearing a bright lip with a dark smoky eye but this goes for anyone, as I think a statement lip would detract from the drama of a smoky eye and vice versa. However, ultimately, you can rock whatever you're comfortable with :).