Even if you eventually perfected the process, It would be much easier to source some horn(even if you pay top dollar), than try what you suggest.
Theoretically you might be able do what you suggest. Hair and horn are both keratin, but horn is very dense and tightly compressed. Its hard to know how much thickness of hair you would need to achieve the same effect as horn.
Would hide glue be the best choice, especially if you need a lot of thickness? Would it become too brittle?
Some type of natural/synthetic hybrid from hair and a modern resin set into a strip, like a piece of fibreglass backing might be viable.
But then is it really all the hair doing the work, or is it the resin?
So I doubt you would be successful just slapping on some hair in glue on the belly, and expecting to get similar results to a traditional horn bow.
The bow might hold together, if it's not too short, but in all likelihood the hair wouldn't be of the correct thickness to properly resist compression, and would just cover up the real damage happening underneath.