I wear turtlenecks sometimes - I have a purple on just as pictured and several other ones in nice jewel tones that I got last winter at Nordstrom for a great deal - I think they look great with longer necklaces. They really pop!
I don't really wear turtlenecks in recent years but when I did I would have to avoid wearing necklaces or leave it under the sweater because I'd forget I had a necklace on and broke a couple of necklaces (mostly cheap ones) that way.