Tim,
I also have an over abundance of olive trees (autumn olive in my case) and I trim them back and chip them up each year. As has already been mentioned, simply cutting them will not kill them. Perhaps if you mowed them weekly or trimmed them the moment they popped their heads up you would kill it eventually, but it won’t go easy.
If you do plant them, I suggest you do so in a place you don’t mind having them for at least part of the year. Once you have them they can be a very valuable source of chips as they have been for me. I have not noticed any allopathic effects and I have them on all of my beds and last year I had one bed composed entirely of chips (mostly autumn olive) being broken down by wine cap
mushrooms. This year, thanks to the mushrooms, that bed looks like crumbly soil. I also have a new chip bed and hopefully a third.
If you want a source of chips, olives are a great option, but bear in mind that they have a will of their own and will grow out of control given the opportunity. Personally, I think this is a great use of your natural resources.
Best of luck,
Eric