I am VERY surprised at the amount of people who have said no!
As has been said, there isn't really a point for the war if cap doesn't die...
In the end, how does the war end? We know Stark can't die. :P
If I remember correctly, Cap was SURRENDURING when he was shot. He was coming to Tony to say, it's not worth it. After he is shot Tony comes out and says the SAME THING! This is the BEST way for an end to the war. Both sides don't think the war is worth it, and one guy gives up so that there is no more bloodshed. Cap dying is CRUCIAL to Tony admitting that he didn't think it was worth it either. We don't want Cap to just go to jail, and Tony looking like a bad guy. We want them to BOTH be good guys. In the end it was just a hard to predict mistake that made Registration a bad idea. Similar to Nick Fury bringing up power to Hydra, no one blamed Nick for Hydra. He didn't become a bad guy just because he inadvertently helped bring up Hydra. Stark is giving more power to an entity that should not really be trusted with it, but he has just as many good reasons as Cap does for opposing it. We've seen where Cap is coming from in TWS, and we will see where Tony is coming from in AoU. Both will have the best intentions. If it went Cap's way, who knows, maybe things would have backfired in the opposite direction. (I haven't read the What If? version, not sure what they do there.)