If a person uses a wood that is strong in compression, say red cedar, but not tension, and backs it with hickory, which is strong in tension, is grain structure of the cedar board as critical?

Can you get away with run-offs and such?

You can get away with a few minor runoffs, but it's always best not to have any at all. It's always best to have what runouts you do have at the tip end of the limbs rather than near the handle or in the working portion of the limbs. There is less strain in the tips than anywhere else in the whole bow.