I don't want to come across like an entomologist, cause you all know I'm not however for me the answer to your hypothetical is yes...but very slowly. Termites do not eat live wood they follow the advances of dysfunction in the tree contained more or less by CODIT...however some termites have an interesting weapon..they farm wood digesting fungi and by doing so actually make available much more wood tissue than would otherwise be the case.
Mycology - Animal Interactions - Symbiotic Interactions Termites' symbiotic fungi & social homeostasis
My own dissections of declining large gums of various species up here certainly suggests there's more going on even with our little (and not so little!) ozzie white ants!