He is under supervision. At least he said to the chess playing guy that he should think of it as part of his surveillance.
But I don't think the let Allen go on missions for his arc controlling abilities. He probably thaught them the song and now someone else is doing that, because in the last page a voice coming from the golem tells them to get ready and that gate 28 is opening. Doesn't look like Allen is doing it.
But you are probably right. It's just that I had imagined something completely different and I am a bit confused. I had pictured Allen under heavy surveillance, maybe alone in a guarded room with his arm restrained so that he couldn't hurt anyone (should he change). And then I read the chapter and he is on a mission.
"For Feanor was made the mightiest in all parts of body and mind, in valour, in endurance, in beauty, in understanding, in skill, in strength and subtlety alike, of all the Children of Illuvatar, and a bright flame was in him"