I think that is the way to play injuries. If I take your hostaging example right here, that can add depth and realism into the situation, because being shot is always a huge pain, even for the strongest character. And besides, if we have good players on both sides of the initiation, can can lead to a second chance for the hostage to make it through alive, by complying this time.
The only problem I see right here - I'll talk with my actual experience - is that some people will just fire away at you, because they know they have a legit way to kill your character. I have no problem with being shot for non compliance, because it's allowed but, roleplaying the bullet injury in a middle of a firefight can be tricky sometimes.
But I'm fully aggreed with you, roleplaying that out right when that happen can add some nice depth to the Roleplay!