Karma (Action) will not dispel the ignorance. Karma itself is based on ignorance Only Self-Knowledge or Brahma Gnana or Atma Gnana will destroy ignorance.
The karma theory is based on the birth entity whereas the Soul, the innermost Self is birthless and deathless because it is the formless, timeless and spaceless existence.
The present birth itself is an illusion because the world in which birth, life and death happen is mere an illusion of the standpoint of the Soul, the innermost Self.Those who believe in the karma theory are unfit to acquire Self-knowledge or Bramha Gnana or Atma Gnana.
The Karma theory is meant for those who are immersed in worldly life thinking the individual life within the particle world as reality. In the path of wisdom, the Karma theory becomes a great obstacle in realizing the truth, which is based on the form,time and space. in reality, the form,time and space is no-existent as a reality.
When Sage Sri, Sankara says clearly, the universe is not real. He says that Brahman and Atman are one. The ultimate and the Absolute Truth is the Self, which is one though appearing as many different individuals. The individual has no reality. Only the 'Self 'is Real; the rest, mental and physical are but passing appearances, then it indicates the form (waking) is unreal the formless is real (Soul). Therefore, only Atman is real because there is no second thing other than Atman.
The individuality is a reality within the illusory world. Therefore, all the theories created within the illusion on the base of false entity, within the false experience, has to be the part and parcel of the illusion. Thus, it is necessary to realize the fact that Atman is the innermost Self and all else is illusion, to overcome the illusory concept of the cycle of birth, life and death. Thus, to understand and assimilate Sage Sri, Sankara’s Advaitic wisdom the seeker has to do his own homework through deeper Self-search, without mixing the religion, the scriptures, the theories, the concept of God and the yoga.
The karma theory is reality only for those who believe their present physical identity (ego) as real, and world as reality. When the Sage Sri, Sankara declares the world itself is an illusion, and Brahman is real, then what value the karma theory has when the world is an illusion, because man is part and parcel of the illusory world. Therefore, one has to view and judge the three states on the standpoint of the formless Soul, the innermost Self in order to overcome the duality, which he is experiencing it as a reality.
Sage Sri Sankara says in Aparoksh Anubhuti: ~ 88. When the whole universe, movable and immovable, is known to be Atman, and thus the existence of everything else is negated, where is then any room to say that the body is Atman?
89. O enlightened one, pass your time always contemplating on Atman while you are experiencing all the results of Prarabdha; for it ill becomes you to feel distressed.
90. The theory, one hears of from the scripture, that Prarabdha does not lose its hold upon one even after the origination of the knowledge of Atman, is now being refuted.
91. After the origination of the knowledge of Reality, Prarabdha verily ceases to exist, inasmuch as the body and the like become non-existent; just as a dream does not exist on waking.
92. That Karma which is done in a previous life is known as Prarabdha (which produces the present life). But such Karma cannot take the place of Prarabdha (for a man of knowledge), as he has no other birth (being free from ego).
93. Just as the body in a dream is superimposed (and therefore illusory), so is also this body. How could there be any birth of the superimposed (body), and in the absence of birth (of the body) where is the room for that (i.e., Prarabdha) at all?
94. The Vedanta texts declare ignorance to be verily the material (cause) of the phenomenal world just as earth is of a jar. That (ignorance) being destroyed, where can the universe subsist?
95. Just as a person out of confusion perceives only the snake leaving aside the rope, so does an ignorant person see only the phenomenal world without knowing the reality?
96. The real nature of the rope being known, the appearance of the snake no longer persists; so the substratum being known, the phenomenal world disappears completely.
97. The body also being within the phenomenal world (and therefore unreal), how could Prarabdha exist? It is, therefore, for the understanding of the ignorant alone that the Shruti speaks of Prarabdha.
98. “And all the actions of a man perish when he realizes that (Atman) which is both the higher and the lower”. Here the clear use of the plural by the Shruti is to negate Prarabdha as well.
99. If the ignorant still arbitrarily maintain this, they will not only involve themselves into two absurdities, but will also run the risk of forgoing the Vedantic conclusion. So one should accept those Shrutis alone from which proceeds true knowledge.
The above proves that the karma is reality only on the base of the false Self, where one thinks body and the universe as reality. When one becomes aware of the fact that, the true Self is formless Soul, then the karma becomes part and parcel of illusion.
My point is that, if one accepts the karma theory as reality, he will never be able to come out of the ignorance. And ignorance makes him believe the cycle of birth, life and death as a reality. Thus the freedom which one is seeking will remain a distant dream. For the one who accepts the birth, life and death as a reality, Self-knowledge or Brahma Gnana or Atma Gnana is impossible.
The path of religion, theory of karma, the path of yoga and the path of wisdom were intended for different classes of people. The wisdom is for the advanced seekers of truth. It deals with the nature of the ultimate Truth and Reality. It is meant for superior aspirants who have an inner urge to know the truth and it is not for those who are immersed in earthly desires.