I am trained as a gemologist and I can tell you that it isn't a good idea to put oils on ivory. Ivory is porous. Oils will tend to be absorbed into the ivory and carry dirt, dust, chalk, etc. along for the ride. I don't think it will structurally damage the ivory but it wil most likely change the color (maybe only in spots) over time. Also I think it's probably not a great idea to get oils on the cue shaft or the tip, which would be unavoidable if you oil your ivory ferrule.
The best way to keep ivory in good shape is to not expose it to very hot or very cold temperatures (like in the trunk of your car, the attic, etc.) and seal it from time to time with a good quality wax, like carnuba. Also, while we're on the subject, oiling opals is a waste of time. Opals are a natural silica glass and they contain moisture of different types. This is what gives them those attractive colors. Opals dehydrate over time from the inside out, which is why they typically develop lots of small fractures. Putting oils on the outside doesn't achieve anything. Probably more than you really wanted to know.