I'm not entirely sure what the steel armature around a magnet consists of, but if I understand it right, it's a piece of steel around the first magnet that gets magnetized by it, in which case it will act like it's part of the magnet. So unless the second magnet is producing an incompatible magnetic field to the first (e.g. they're in north-to-north configuration), then, no, the second magnet should not impact the armature.