The quick answer is no. The more involved answer is that the level of restriction depends on the type. Mammoth and mastodon ivory carry no restrictions because they are from extinct animals.
Ivory is a natural tooth substance that continues to grow throughout the animal's life.
Artificial ivories do not have this kind of structure, and are usually a consistent color throughout. I suggest you check these links out if you have questions. Heat a pin to nearly red hot and touch the tip to an inconspicuous part of the object. If it is polymer or celluloid, the pin will melt into the piece, and smell like plastic or bakelite burning. For one, I do not consider plastics to be environmentally friendly.