Will copper wire with a non-tarnishing coating be insulated?
Probably it's a lacquer coating if it's a crafts type wire so it would suffice for a very low voltage. 

You can take a couple pieces and twist them roughly together and see if you can measure any continuity between the two. You'll need to remove the coating at the ends to make a reliable connection- soldering heat may well do the trick if it's a polyester lacquer. Be more gentle when you wind the actual coil, obviously. 

One manufacturer states that: 


  The tarnish resistant feature results from an oven-baked clear coat finish