Even WITHOUT any wood - many common charcoal brands have their own "flavor-signature".
I find that K-Blue Bag has its own type of smoky flavor, due to the stuff that's in it. I like it with some stuff like steaks / pork, but not so much with other stuff (poultry / fish)
Generally - I find that ALL-Hardwood Lump tends to be more flavor-neutral, meaning that I can typically use more smoke wood than I would with typical commercial briquettes. In particular - Cowboy brand seems to be more neutral, perhaps because it seems to be made mostly from kiln-dried hardwood scraps (I would bet that they buy scrap from commercial cabinet makers, etc.) instead of "raw" lump like Royal oak, which seems to be made from charred whole logs with bark, etc.
You might want to experiment with bare charcoal of different brands with something inexpensive (like yard bird) and see what you think of the various flavors from different brands. Then, based on your findings, you can "tweak" the amount of smoke wood, if any, that you and your family prefers with different meats.