Iron Kettle Belly is a hell of a mutation, and there are others that are similarly profound in ways that WH40K mutations tend not to be.
Also, mutations don't generally offer the level of power boost that cultivation clearly does.
I don't see why it wouldn't work similarly, assuming we are in 40k and everyone else are just psykers.
If we the theory is true than I would guess cultivation is something like that, a combination of self inflicted spiritual mutations, the consumption of other beings' spiritual power in a way not dissimilar to how demons grow stronger and biomancy.
The difference between warhammer mutations and cultivation being that one, cultivation isn't made to the whims of the chaos gods, meaning that when you mutate yourself, you do not develop useless mutations who drag everything else down, you slowly make yourself into a higher being, like the difference between Ork machinery and actual technology.
For another, pill making allow you to add more to work with for the whole, you incorporate more material, spiritual, chemical, genetic, rebuild yourself, and use your new better self to make a new better self, like seed AI.
You are the ship of Theseus, slowly replacing each plank until it is functionally a new ship.
Chaos champions don't have that, they have the gods giving them booms without any thought to the greater whole, breaking apart their mind, removing from most the purity you need for a dao and replacing it with their own, and the gods don't necessarily want to give people that power.
Can Tzeench make someone an alpha plus psyker? If he truly wanted to? I would guess the answer is yes, he just doesn't want to.
Speaking of cultivation in 40k
Here is a case of what seem relatively similar to cultivation
Few beings in the Screaming Vortex can claim to have impressed the Lord of Dark Delights with their conceit, their vanity, and their hubris. Those who do typically earn the jealousy of Slaanesh, not admiration, as such things are beneath the god of indulgence and self-obsession. However, one being caught the eye of Slaanesh and received a nod of true admiration. In her struggle for self perfection and vainglory, Ax'senaea, called the Thrice-Possessed, damned her people to eternal anguish and impressed even the Prince of Excess.
Long before the days of the Angevin Crusade, while the Calixis sector languished beyond Imperial control, the planet of Laodomida spun its lazy orbit around a star in what is now the Drusus Marches. A system far from any other, Laodomida was an isolated place of planetary intrigue and politics. A world consumed with its own extravagance, the intrigues of the ruling class were usually harmless enough, occasionally devolving into dynastic assassinations and scandals, but rarely all-out warfare. Into this world was born Ax'senaea, last born child of a minor noble family.
By her third decade, the woman who would end her world had spent her entire life among the courts and war-rooms of her powerful kin. Oft-ignored in favour of her more aggressive siblings, Ax'senaea was left to turn inward and ponder the darkest regions of her own soul. Seeing her position, forgotten among her rivals, as little more than a matter for self-improvement, Ax'senaea quickly rose to power by mercilessly removing her competition. In only a few years she had decimated her dynasty and seized control, while keeping its holdings intact. It was not enough for the newly-minted Executrix Primaris, though—she still had too little control over her world, her own psyche.
Believing them to be manifestations of her own skills and knowledge, she collected a court of learned sages and strategists, putting each to death after she mastered their knowledge. Among these men was a secret sorcerer of Chaos. Hoping that it would end in her death, the sorcerer taught Ax'senaea the process by which to bind a powerful servant of Slaanesh to her own soul. His plan—that the despotic woman could not hope to command such a creature—was foiled by her overwhelming will and self-obsession. Though the ritual was long and exhausting, Ax'senaea was able to crush the daemonic entity beneath the weight of her indomitable will.
Now possessed of the power of a Keeper of Secrets, the vain woman murdered the sorcerer and slew the remainder of her cabinet. She used her newly acquired warp-sorcery to exert more direct control over her subjects and her enemies, twisting their minds to her will, driving them mad with desire or jealousy, or eviscerating them with a thought. She continued to abuse the daemon within her for decades, draining its essence to fuel her ambitions and maintain her youth until she consumed its power, banishing it back into the Warp and binding a new Keeper of Secrets within.
Over the following century she consumed a second and third daemon entirely, and plunged her world into utter chaos and conflict. She corrupted the souls of the ruling class the world over and spurred the populace to acts of subservience and adoration, sacrifi ce and murder, all so that she might prove the control she had over what she saw as her own psyche, her own body and mind. When her world was entirely under her own control, she spread to the other in-system planets, conquering, dominating, and commanding the countless billions touched by her infl uence. When the third daemonsoul withered and vanished within her, Ax'senaea performed the ritual yet again, hoping to devour the power of a fourth greater daemon. It was then that Slaanesh granted the woman daemonhood, both out of disdain for his most powerful servants and in adoration of the woman who had twisted the minds and souls of billions with her dark perfection.
Pulled into the warp by the possessive jealousy of Ax'senaea herself, its puppet-populace living out her every wicked excess, Laodomida now spins aimlessly through the warp, a world re-formed daily by the fi ckle whims of its insane mistress. Despite the gifts of the Prince of Pleasure, Ax'senaea remains mad, consumed by her own self-obsession and solipsism. Her deranged mind has now turned to the beings of the warp, and to her mad eyes they are simply rebellious aspects of her nature, needing to be controlled as much as any world in realspace.
So basically, a girl entered a mind match with keeper of secrets, broke it, tortured it and drained it's essence to extend her life and increase her power, and than did it again two more times, until slannash just granted her demonhood.
She never even worshipped slannash or something, as far as we can tell, she is still certain that slannash and all the chaos gods are just rebellious parts of herself.
Her iron will and certainty in her own superiority transformed her from a mortal into world conquering psyker, when given the right resources, who know, maybe she would have ascended on her own merits had slannash not interfered.
Big E almost decided to ascend to fight Horus before he was convinced it wasn't worth the cost (he would become the dark king, a chaos god) and he abandoned his ascension to face Horus as the underdog.