Filling with sawdust and glue won't hurt.
You never know. It could break.
Of course sinew and rawhide are a possibility. Sinew is time consuming. To do it on a bow that may break...I don't know.
I remember an osage bow I made with a worm hole in it and I also remember a hickory bow with a worm hole in it.
They didn't break.
I also remember a hickory board bow exploding because of a tiny knot I didn't see when buying the bard.
You just never know.
Jawge