Slide-on and Strap-on quivers don't put any stress on the limbs in the fade out areas. If mounted correctly, they would be above the fade outs where the limbs don't flex much.
If you're thinking of doing it on a longbow, there's not a lot of riser to work with, and the quiver bolt holes for a two point quiver will likely be relatively close together, which means the hood and arrow gripper will be fairly close together, which in turn can flare out the arrows in the quiver. Also, because so much shaft is protruding below the lower gripper, they may vibrate quite a bit and the fletching even hit each other, creating noise.
Regardless, if you're set on a side-mounted quiver, go ahead and drill. Use a drill press though to get the holes in straight. Doesn't hurt to also use a tap and die to start the threads (if that's the kind of insert you'll use). Otherwise, there's a good chance the threads will chip out some wood around the holes. I've seen some real hatchet jobs. Good luck.