Coral Tree. Full grown. How would we know if white ants are eating from the inside and can it be treated before we remove it.

Question

See above

Answer 1

Ants are not known issues with Coral Trees.
Moths are a known pest.
These links may help you identify the issue with your tree.

http://ucanr.edu/blogs/blogcore/postdetail.cfm?postnum=20988
http://ipm.ucanr.edu/PMG/GARDEN/PLANTS/coraltree.html