It is described as nicca, unchangeable "stage" if reached, but since all Dhammas are anatta, it would be not unconditioned proper to regard it as such (atta), and the Buddha would have (like popular movements, Dhammakaya in Thailand for example and many individual teacher, doing laypeople a favor with such notion) easy more followers, since beings delight in "being".
Of cause one can call it "true"- Self, if one seeks sense or Self in it. But it would not hold. If understanding "real self" as senseless, meaningless, as like somehow "aṭṭa", than it will probably hold.
Consider the three meanings of aṭṭa carefully, high confussing or giving realese. Since one might see the base of atta and anatta, as a "game" of perceptions, stands.
Certain Brahmic-Attman- and certain Mohayanic-appoaches, are dangerous, had lead to bad thing in history, on it's account.
The Dhamma of the Buddha is not taught for certain Self-seeking, true self-purposes, but to get free from suffering. He rebuked a "rebelling" monk who said, "if you don't tell me if there is a Self or not, I will return to lower life", with asking himn "Did I ever told you that I will regard this matter, will ever teach such, as you ordained?"
(Careful read and proper attention was required to understand, for the case not, not grasp the message, after the finder, not looking at the moon)
[Note: This is a gift of Dhamma, not meant for commercial purpose and other low wordily gains by means of trade and exchange]