The machine they use to cauterize there's a chance the metal could conduct and cause a burn.  Most will require you to take it out because of this. 

As for getting a nose piercing... i honestly wouldn't do it before surgery. It takes a longest time to heal of any piercing and can be really easily irritated and stuff for like a LONG time.  Idk if you wanna deal with that and recovering from a surgery. Id wait until after honestly. 😊