It might survive tillering, or even for a decent amount of shooting but it will pop rings on the back eventually.
I have also seen bows from staves like this go during tillering, especially in staves with thin rings that look on the end grain like predominantly early wood.
Nice experiment and I can understand why you might want to try it out, but it has been tried by plenty of people in the past(including myself), a rawhide backing before tillering will save the stave, and save you time in the long run.