Immanent critique is a practice entirely distinct from (New Critical) formalism's holding that poetic language should be considered as autonomous from the knowability of an author's intentions and from its conditions of production. Neither is it an Adornian concept.
Rooted in Hegelian Marxism, the practice is made explicit by Adorno and Horkeimer writing together in The Dialectic of Enlightenment. The book is a critique of the Enlightenment using Enlightenment methods, which defines the concept of immanent critique: "the theory that adequate description and criticism of a philosophical or cultural text must be carried out in the same terms that text itself employs."
Immanent critique is, thus, in no way proposed as a way of understanding art, much less poetry, in particular. And it surely doesn't mean to understand art as art, as self-sustaining and autonomous object. A central goal of immanent critique is rather to uncover the internal contradictions of a philosophy or text objectively, rather than incidentally imposing the inherent contradictions of a pre-determined method or ideology. This uncovering is done exactly so as to reveal the impress of social conditions on the reputedly but not actually objective or autonomous philosophy or text (and specifically, as articulated by Marx, Lukacs, Adorno & Horkheimer et al., the contradictions and deformations of capitalist relations). "As pointed out by Lukacs in his History and Class Consciousness, the essence of immanent critique is therefore dialectics." Which reminds us that it means to understand its object not as an aesthetic object but a historical process.
The frictionless, immediate, and unremarked slippage from immanent critique to intentional fallacy is a useful index of the problematic of enlisting partial concepts from one philosophical practice to bolster a quite different aesthetic claim. Indeed, to register this very slippage in recent discussions on the Poetry Foundation's blog might well be the beginning of an immanent critique of the ideologies objectified there.