dont think whether its carbon or not matters from a glue adhesion perspective- as they are all set in a resin matrix- , and that is what the glue is adhering to.
have seen folks doing it on glass bows all the time, and using both TB 2 and TB 3- i would personally go with TB3- and seal it all well.
how it will effect performance i dont know- but - and i am probably wrong here- but i think the main reason for using carbon is its inherent stiffness, "increasing the bows ability to return to its original position quicker"- in laymans terms. i think the reduced weight is a contributing positive aspect, but as a stand alone characteristic it would not add enough performance enhancement!!
sure some more experienced folk will also clock in soon!