Very possible. Though there's no way he'd tell Matt that, because that would let him know he was looking after him, which Matt would hate. Maybe this could all come out when Stick turns up and tries to get Matt to do something for him, and Mike gets all defensive and insists he goes instead, or alone if Stick has planning on sending them both. Stick might say something about how he has let Mike think he was getting away with protecting Matt all these years, but enough is enough, Matt overhears and isn't happy about it, leading to a talk/fight later when Stick's not around.
Re: Where Matt has a real identical twin named Mike who is sighted and is Daredevil