Cutting palm roots will damage most palm trees. If you dont do siginificant damage then you might get away with it, but if you are cutting large portions of roots, then you will see growth of the palm tree snow and it will weaken (which could make it prone to rot, fungus, and disease. I would avoid damaging the roots as much as yoy possibly can, but if you do, make sure it does not see any stress (drought, cold, extreme heat (especially if it includes drought, ect...) for at least a year.
Good luck!
-Alex

Thanks Alex. Do you know what type of root system Christmas Palms have? Does the roots tend to grow down deep into the soil or most stay along the surface horizontaly?