It might depend on whether we are talking about American termites or Australian termites.
Some termites are bigger than others, you know.
I wouldn't be surprised if they do good things for trees and bad things.
They do destroy solid wood. And solid wood in a tree is not a bad thing to have present, even if it's dead tissue. There is going to be some strength in it, unless its burrowed and digested.
But that may be more a matter of weakening than killing. Yet, weakening can lead to death.