Certified GKH Gardening Expert
From my research, it doesn't appear that the roots are highly invasive. However, if you are ever in doubt, then it is best to avoid planting this in an area where it would cause damage. It is completely up to you. I don't believe it would cause any damage, but I always err on the side of caution.
Here is an article for their care: https://www.gardeningknowhow.com/ornamental/shrubs/toyon/toyon-plant-care.htm