No, the inner bark will not work as a backing. As a rule, cloth or fiber cordage backings will not prevent string follow, but are useful in keeping the back from raising splinters. If you keep to a single growth ring on the back, this is a minimal concern. Sinew or rawhide will help keep string follow to a minimum. If your bow is designed and tillered well, however, no backing should be required, especially with well seasoned hickory. If you do have any doubts, though, it is best to use some kind of backing. It will only add to the durability of your your bow.