In short I would say NO.
Spanish moss causes little to no detrimental effect on a host tree. It may appear to have roots growing within the host tree, but it is an epiphyte. Epiphytes grow on other plants without taking any water or nutrients from them, and use the host plant for support and protection.
Alot of people will still say that it leaches nutrients and water from the host tree, but I have had this stuff growing on all my tress in my yard growing up as a child and it never caused any problems.