Its probably okay to try and shoot as long as its structurally sound, and its slowly retrained. Problem with old bows that they get broken by ignorance, as the vast majority of people(not people who frequent this site) have no idea of what they are doing. I personally wouldn't do it because its a waste to risk something original, and authentic. At some point if a bow keeps getting shot it will break.
With a bow that might be historically rare or valuable it is probably better to have an experienced bowyer make a copy of the design.
I personally have shot old bows that probably shouldn't still be shot. They were vintage tubular steel bows, they had a reputation for breaking from metal fatigue and rusting in the internal tubing. I was warned not to risk shooting them.
Fortunately none of them broke, but after I realised they were very mediocre performers, I lost interest in shooting them anyway. I feel they are better as curio's, left intact rather than as broken junk.
Most of my antique wooden bows(especially yew) have scratches, bruises or other dings on the back and I know it would be too risky to try shooting them. The funny thing is many of these old bows don't follow the standard information we have been left in books. Differences in limb design, handle lengths and layouts, nock design and other small nuances are apparent. Bows that have been layed up in billets with intentional deflex yet haven't taken any more set along the limbs that you would usually expect. Some of these old bowyers really knew what they were doing. It would be a shame to lose this kind of information.
Also that "ivory " strip does not look like genuine ivory to me, because of the series of parallel lines running down its length look too even, like some kind of manufactured synthetic.
Hamish.