TB isn't truly water proof. They use the term very loosely. It is very water resistant. You are going to wind up sealing the bow anyway to protect the sinew and the wood. So why not get the most out of the sinew by using hide glue or Knox gelatin, then after it is fully cured seal the bow.
Another thing to think about is by applying with a water resistant, or even worse a water proof glue, how is the sinew going to fully cure. If the outside of the glue dries before all the moisture has left the sinew, it could take a really long time to fully cure.