WILL IT TARNISH?

Yep.  Copper does tarnish.  It reacts with chemicals in the air, mainly sulfur and forms a patina.  Some people love their copper patinaed, there can be a lovely array of blues, purples, bronze and gold tones in tarnished copper. 
Copper is amazingly easy to keep shiny and new-looking though:

When you take off your piece, place it in a zip-locked plastic bag or tarnish cloth. 

Tiny spots on flat parts of a piece can be removed by rubbing gently with a pencil eraser(yes, this works, try it on a penny!).

Or call in the big guns:  squeeze the juice of a lime into a pan of water and soak your piece until you can see it shine again.  No rubbing required though you may have to watch for pieces of lime pulp.