The bark protects the cambium so if you remove the bark and the cambium stays behind(not likely) it is exposed to the elements thus damaging and killing it.
I think the cherry bark(choker cherry) I used was taken from dead trees. I'm not sure which cherries have bark that is useful for bow backings. Choke cherry was also used as a binding material. Since it peels around the log(instead of lengthwise) you are limited to the length you can harvest for backings or whatever.