I have seen it done in rifle stocks for strength and stability. Cut a thick plank down the middle, swap sides, and glue back together.
In slender longrifles, I believe it would make a stronger rifle if the right glue joint is made.
I would certainly stain both mating sides thoroughly before glue work, as glue does not take stain.
I think with the right "antiquing" and careful planning of the tang, butt return, and toe plate, it would be nearly invisible. Especially with a wear plate.
There is a modern rifle company now that offers a stock made this way, and it is hardly visible, but stronger and resists moving and warping. Best wishes, and God Bless, Marc