The answer has to be no, clearly not. A Possible alternative (thus excluding necessity): moral behaviour is only insofar it is (considered as) moral. Otherwise, it's just behaviour
As Rebecca Kukla insightfully argues in the context of the famous "Myth of the Given" with an argument based on Althusser (Althusser, L. (2006). Ideology and ideological state apparatuses (notes towards an investigation). The anthropology of the state: A reader, 9(1), 86-98.), normative facts have a mythical constitutional history: They "are" only insofar they are recognised, although they are recognised as being inherent to persons and/or behaviour. This kind of ascription of normative facts to behaviour and persons is only possible after the fact of recognition of these normative facts as (normative) facts, though. In other words: The recognition of normative facts is constituting the normative standards as facts which only after their constitution can appear as if they would have existed before the recognition constituting them.
What does that mean? It means that regarding normative facts, the story goes as follows:
1) We are hailed/appalled by behaviour that (as we will later think) "implies" a certain normative status we actually do not have at the moment when this is happening. This means neither that there is normativity implied in the intention of the behaviour (only that it can be thus interpreted), nor that the normative status must have existed at that moment (e.g.: punishment because I am responsible for my bad behaviour of theft)
2) We respond according to the normative framework embodied into this hail and thereby recognise it as authoritative (e.g. I make sense of the punishment as being tied to my theft as "bad", i.e. I "take" the theft to be "bad" as I link it to punishment - the intentions and factual dispositions and desires of the punishing person are of no importance, but usually realised through this "recognition")
3) Thereby, the normative fact about my person/the world implied is acknowledged/recognised as having been true from the beginning, although it is factually constituted only by my recognition of it (e.g. Only because I agree that this is bad and I should have known it, I become responsible - even if I could not possibly have known it or be a person that is to be held responsible when I have done it)
4) In hindsight/memory, all experience is evaluated from the standpoint of this normative fact as an always-already, e.g. I think in hindsight that what I did as a kid was "bad" although as a kid, I did not know/recognise the moral standards I now am able to use after I recognised them. Kukla - with Althusser - calls this "misrecognition", i.e. I recognise myself as "objectively" always having been subject to these normative facts. (e.g. Having learnt the normative facts, I remember myself having done bads before and feel responsible for it although I have not known or felt this way back then)
5) The problem is: We who can speak about normative facts are all already in a status of thinking and acting in the "Space of Reasons" and must think of actions in terms of normativity. Even if they are factually constituted by us as having authority for us (probably around the age of 4), automatically ascribe normative facts to things in the world although they are nothing inherent to the physical world and its causes. Therefore, any justification of objective normative facts is necessarily "mythical".
6) In a very important sense, normative facts, therefore, have no independent being, i.e. do not exist. They are only from the moment on and insofar we acknowledge them as such.
Source Kukla, R. (2000). Myth, Memory and Misrecognition in Sellars' "Empiricism and the Philosophy of Mind". Philosophical Studies, 101(2-3), 161-211.
An important point Kukla stresses here (with Sellars) is that claims about normative facts follow a logic different from claims about facts about the world in that their authority exactly does not rely on existence.
Recognition and consequences
Now, addressing the comments, the argument can be turned against the proposed transcendental structure:
If normative facts are constituted by a recognition as such, they can without a problem be ascribed to counterfactuals and imaginary entities: The "existing" behaviour of Carl the mischievous (existing) child "is" no more moral than the "imagined" behaviour of Carl the mischievous (imagined) alien if both are evaluated in moral terms and thus recognised as morally relevant. Even if the former certainly very much is while the latter is not.