IF, and that is the really big word in this sentence, there is a growthring that you follow from end to end without leaving you with one or both limbs paper thin, then yes, it can be done. But it would be an extraordinary board.
I have made several board bows to look like stave bows just by adding a little crown to the back of the bow. In those cases they were either sinew backed or rawhide backed, too. If you go to the Little Big Horn Battle site, they have a filmed re-enactment of the battle...the bows I am speaking of are in that video.