If it was mine, I would have glued and doweled or screwed the two pieces together. A nice hardwood cap would hide the hole in the bottom of the pistol grip.
The pictures show that the way the grain is running is very weak in that area and could do with re-enforcing rather than rely on glue alone.
Some old 10m guns I have, have vertical hand grips with a near horizontal grain which would be very weak if it was not strengthened with a hardwood dowel from the factory.
I would have a go at it especially if you intend to replace with a new stock. Its a good way way to learn a new skill in wood repair. You could always paint it afterwards if it shows too much. Good luck with it anyway.