May Sei sense magic on your character? How much do you want him able to tell? Sure! Castiel's used to being recognized by supernatural creatures.
May he use this information to be a jerk to your character? You bet.
May Sei's singing voice have a soothing effect on your character? How much? I'm leaning toward yes. There might be a few instances when it won't work (like if he's going full avenging angel) but Castiel can be affected by magic, especially if he's been weakened, and the guy thinks sitting quietly's fun. So he won't say no to some soothing relaxation.