It is quite possible that connections between Hegel's Absolute Idealism and (some sense of) realism can be drawn out. But there is a fundamental divide between the two in the or a standard sense of 'realism'. It develops as follows.
Realism in most forms assumes the existence of a mind-independent world of which we can have knowledge. So for realism, mind and world are distinct. For Hegel, by contrast, any divide occurs not between mind and world but within mind or consciousness itself.
The following comments by Preston Stovall on Tom Rockmore's book on Hegel is helpful in explaining this view:
Rockmore's central claim is that most analytic philosophers commit themselves to metaphysical realism, or the belief that our knowledge grasps hold of a mind-independent world, while Hegel is committed to a wholly historically bound and constructivist theory of
knowledge. (Preston Stovall, 'Hegel's Realism: The Implicit Metaphysics of Self-Knowledge', The Review of Metaphysics, Vol. 61, No. 1 (Sep., 2007), pp. 81-117: 86.)
The central evidence for Rockmore's ... reading
of Hegel is culled from the Introduction to the Phenomenology of
Spirit, where Hegel discusses a criterion for knowledge (the problem
of how we know that we know) and the extent of the coverage such
knowledge can hope for ... . The point of departure for Rockmore's claim that Hegel rejects metaphysical realism seems to be Hegel's assertions in sections 84 and 85 that "consciousness provides its own criterion from
within itself, so that the investigation becomes a comparison consciousness with itself; and that "Notion and object, the criterion
and what is to be tested, are present in consciousness itself. .. [thus]
we are also spared the trouble of comparing the two and really testing
them, so that, since what consciousness examines is its own self, all
that is left for us to do is simply to look on." This line of argument is
interpreted by Rockmore precisely as the renunciation of knowing the
real world as it is. He writes, "[S]ince the distinction between subject
and object no longer falls between a subject and an independent object, but rather within consciousness . . . the relation between reality
and appearance . . . has been resolved." ... "[I]n the
introduction to the book [the Phenomenology], for the canonical opposition between subject and reality, mind and world, or consciousness and what lies outside it, he [Hegel] substitutes an opposition within consciousness."
(Preston Stovall, 'Hegel's Realism: The Implicit Metaphysics of Self-Knowledge', The Review of Metaphysics, Vol. 61, No. 1 (Sep., 2007), pp. 81-117: 87-8; Tom Rockmore, Hegel, Idealism, and Analytic Philosophy (New Haven: Yale University Books, 2005): 23,
219, 221 and 222.)
The references to Rockmore do not do justice to the full detail or the direction of his argument but they do serve to indicate the distance and divergence between realism and Hegelian Absolute Idealism.