We don't know enough about balistic tech or arrows to rule either way.
But, I can tell you from my modern firearms knowledge that just about any round fired from gun is going to be destroyed on impact. This is simple science and phyics. The rapid decleration from inpact causes rounds (even Full Metal Jacketed rounds in some calibers) to warp an fragment, rendering them useless.
If you use a high powered bow with an arrow with a weak spine, it could shatter under the stress of the energy transfer. Too stiff of a spine, and the arrow will not fly correctly.
As to arrow recovery, I asked a bow hunter buddy of mine. He said he can usually reuse an arrow after hitting an animal, provided that the animal doesn't break it when it runs or falls. Apparently, dropping a larger animal like a deer in a single instant kill is very rare. Most often the strike is a mortal wound, but the animal bolts and runs on impact, dying of blood loss, stock and or organ failure minutes after the hit. (My buddy told me that generally after you land your hit, you just sit and wait for 10 minutes before tracking the animal down and finding where it collapsed, usually a couple hundred meters from where you shot it....
So yes, it could be possible to recover your arrows based on what he said...... at least some of the time.
And believe it or not, hitting a soft target (like an animal, or person) causes even more structural damage to the round.
Arrows on the other hand have different issues. And I am not an expert with bows; That's not to say I havn't used one. I have in fact used traditional bows from 3 seperate contenants, an english traditional made war bow, a sewswepmich trail bow, and a Ghana hunting bow. (I just freaking suck with them)
The problem faced with bows and arrows is the rapid transfer of energy from the bow to the arrow causes the arrow to flex in flight (known as the archer's paradox). This even happens with center fire bows (which most new bows are).