Yes, TBII will work as well but it is only water-resistant not water-proof.
There are two things I don't like about using TB glue with sinew. One, if the sinew is wet, the glue will weaken when it mixes with the water in the sinew so you'll have to use slightly damp or dry sinew. Two, there isn't much time to lay down the sinew before the glue starts to dry. Once it starts to "clump", the glue must be allowed to dry for about 30 minutes before you can add another layer on top. You've got to work very fast. It's designed for production work. You can't just add water to extend the drying time like you can with hide glue.
I've used wood glue and sinew for hafting and it works well. I have not used it for backing a bow. I prefer to use poly-cotton thread with wood glue when backing a bow. The thread is easier to work with and can be any length I want.
Hide glue will set up or "gel" quicker than wood glue unless you are working somewhere that is 95 degrees or higher. I prefer fish glue over hide glue. Hide glue drives me nuts, but that's just me.