Conceptually, I think the idea of making a unique, high-tech bow for your players to choose from amongst the other 40k weaponry isn't a bad idea.
Thing is, there isn't much you can do to improve the design of a bow (beyond making it more durable) without changing it into something that isn't a bow. You are still going to be limited by the strength of muscles (or bionics) in the person using it and the flight characteristics of an arrow.
Though if you are talking about a bow wielded by someone with Space Marine or Ork strength, and have a bow that can handle it, the bow can still be reasonably powerful
The problem is that you're presenting weird anecdotes from hundreds of years ago as rational as to why a society with the kind of tech like 40k would still use bows.
That is only a problem if you are trying to claim that using a bow is a good idea. I don't. Instead I start with a rich eccentric for whom using a bow is more important than having an effective weapon, but he won't argue with ways to make his bow better.
Not to mention a few mechanics no one has discussed: This person, firing 3 arrows on SA in a combat round, how much ammunition for that are they going to be carrying? How much can they shove in a quiver? Seems like they'll run out pretty quickly, and it's not easy to have a few extra quivers as spare.
It was only two arrows. Though you do have a point here, even using a bow we are talking about 0.2kg per arrow if you use the clip weighs 10% of the weapon rule. That is some heavy ammo.
If this comes up in any of my games, as long as the player has the carry capacity for those arrows, I won't ask about how he carries them.
Also, a major bonus for arrows is that being wounded by one is an incredibly traumatizing experience, as you now have a shaft sticking out that does just about as much damage coming out as it does going in.
What should the threshold be for the arrow getting stuck in someone ?
I'm not one to say that a wound must mean an armour breach, it could have just been an impact that really knocked the target around while still bouncing off his armour.
There will some arrows that don't get stuck. For example exploding arrows will explode, meaning there isn't any large part of the arrow left to be stuck inside the target.
All this said, you should concentrate more on presenting this as a specialized weapon, one that kills silently and in specialized situations, rather than something to be seen alongside of stubbers and lasguns in an underhive.
As a weapon with a potential free action reload, being able to chose the best ammo for the task (instead of just loading up with a general purpose ammo) is quite possible. We just need to come up with some interesting arrows.
So what kind of specialised arrows can you think up ?
Since a strong arrow will be reusable, and daemonic weapons are very durable, daemon arrows are a possibility. Unlike a daemon bullet, which will probably only get used once and will be very suspicious if the character tries to use it a second time.
Nasty thought: Target has a power weapon and deflect shot. You have a daemon arrow. You shoot the target with the daemon arrow, they parry and break it, daemon gets loose