So the next step is Angel the Pippin is dead, and Hope or the radio has been shot? Yes, if he had not ran to check on the armory, they'd be alive. But maybe you're forgetting,
the armory alarm had been tripped. The armory had been raided before, and the rat had stolen all of their supplies. When the alarm was tripped, the first reaction of any soldier, EVEN the infallible
Michael would have done the same thing. The logic behind it is simple, Pippin was chained to a wall, he wasn't going anywhere. The armory on the other hand was possibly being raided by the traitor. The best choice at that time would have been to run and check out what was happening at the armory, and possibly find out who tried to break in. The armory is on the same floor as the guard room, and I believe they are both on the second floor. Well the majority of the tower has relocated itself to the 5th and 6th floors of the tower after the fire, so there is a very good chance that Angel was one of the only ones who were in the vicinity to hear the alarm go off. So basically, best decision he coulda made was to check out the armory rather than keep guard over pippin, because no one could have assumed that pippin would fall under attack. The only logical move in that situation was to go check on the armory.