Necklaces can work in a headshot if they are centered, not too long, and not too large so they become distracting.
Jewelry in Headshots:
When getting Headshots taken, it is ideal to keep the hereof do a. Minimum. The reason for this is because it can be distracting and can draw attention away from the eyes. For actors, the general rule is no jewlry whatsoever. For non Actor's, jewelry isn't as big of a problem if it's used sparingly in a way that supports the look instead of drawing away from it.
Earrings should be small and minimalistic, and definitely stay SY from hoops. The larger the earring the more distracting it will be and the shine will draw attention to itself. Another issue is that depending on the length of your hair, it will likely cover the ear completely so you won't even see the earring.
Make sure to never put your hair behind your ear in a headshot because it will draw too much attention! The ear just sticks out distractingly, so I decnintely recommend covering it.
In regards to necklaces, less is more but think about how it balances what you are wearing. Ideally, you wear a simple top and the necklace supports it. But if you are wearing a busier top, you may need a thicker necklace so it doesn't get lost and seem out of place.
The neckline of a shirt is very important and needs to compliment the necklace that is warn. What do I mean? Well, if you wear a shirt with a deep neckline and the necklace is very long, it can give you a stretched out feeling where the neck seems to long. Likewise, wearing a very short neckline and/or necklace can feel constricting like you're being cut off. A necklace that is too long can easily be shortened by pulling it back with a clothespin, but if it's too short, it's much more difficult to make it look good.
Necklaces can essentially create a neckline for someone, which gives a nice structure to clothing and makes the shot look more natural.
Ideally you wear a necklace that comes down about 3-4 inches from the base of the neck. More than that is too long, and less is too constricting. A shirt neckline should come down about 4-5 inches for women.
Another vital thing is to be sure that the necklace is centered properly in the shot. Sometimes this can be overlooked if you're not careful, especially because as you turn your body to the side, a centered necklace will no longer be centered in the shot and will need to be cheated over.