Getting a lip pierce and neck tattoo 3 weeks before oral surgery?

Please don't. What's your hurry? Have the oral surgery, recover from that, then abuse your body any way you want, if you're so inclined; it's a free country. But why do anything just prior to a surgical procedure that might complicate that procedure, due to an infection or other issues? Why take that chance when it just isn't necessary?
Please don't. You run the risk of instruments catching on the piercing. If you were my patient, i would ask you to take it out to prevent this risk.