Bob Jewett said:
You might be able to see the grain under a magnifying glass. You could also visit a local jeweler or Asian art store and ask their advice.
At any rate, there is probably so little ivory in the cue that the material cost is unimportant. I suppose that the presence of actual ivory might indicate a more competent cue maker, but maybe not.
There is a lot of plastic used that resellers claim is ivory but is not. I have found that inlays that are solidly or very evenly colored are not ivory. Ivory has varied grain, color variations, striations, etc.
However, the high quality synthetics look exactly like ivory. I have a Paul Huebler Custom Shop Ivory Twist cue which has the exact color and grain of tusk ivory, yet is made with synthetic. Some of Meucci's synthetic ivory joint collars and ferrules would fool anyone. Many people confuse the smokey, creamy look of buckhorn with tusk ivory, and bone looks completely different than elephant tusk.
"The Book" is right. To test for real ivory, if it means a lot to you to determine if it is ivory, hold a needle in pliers and heat it on a stove until red hot, and stick it in the ivory. If it's ivory, it will not penetrate but will leave a small mark. If it's plastic, you will have a pin hole.
Since the cue obviously doesn't have a history, documentation, or markings, it is unlikely it is real ivory or worth much.
Chris