It's actually more than possible. In he manga, during the “Goku Black” arc, Goku actually uses “Hakai" against a merged Zamasu.
While Goku would be unable to survive a true Hakai blast as seen in Dragon Ball Super, it seems as though he can survive the weakened version of Destruction Energy. Beerus did save Goku from this energy in the end, yet the Saiyan showed no signs of being unable to handle the energy himself.
With the addition of Fused Zamasu from Season Pass 1, Beerus will also use the Hakai on Fused Zamasu as well. In Heroes, Super Saiyan Blue Goku can use the Hakai. In Dragon Ball Super Card Game, SSB Kaio-Ken Son Goku, Concentrated Destruction also uses the Hakai as an auto-ability.
Like his Super Saiyan and Super Saiyan Blue transformations, Ultra Instinct was susceptible to Gokū's rage, allowing him yet another explosive increase in power and speed whenever Jiren angered the Saiyan.
What if Goku tried to Hakai Beerus? If Goku did that(and obviously this is Manga Goku), nothing would happen because according to Beerus, Hakai doesn't work on immortal characters and Bills is immortal.
For years, anime fans have questioned whether or not Goku can beat Saitama, and he most definitely can. After achieving his Perfected Super Saiyan Blue form, Goku gained the ability to use Hakai, which is used by Gods of Destruction to erase beings from existence. Even Saitama cannot survive such an ability.
According to the latest manga of dbs, there are still forms of ultra instinct left for goku to achieve, like the one which grand priest uses. And ultra ego is still just the same as it was before. Even though in power, UE wins.
In summation. With the information currently available, it seems that Ultra Instinct Goku would be the winner if this Dragon Ball fight were ever to happen. While Ultra Ego certainly wins out on offensive firepower, Ultra Instinct's defensive abilities and potential forms likely outstep Ultra Ego on equal levels.
During the Tournament of Power, Goku managed to gain the powers of Ultra Instinct, and during the Moro arc, he learned how to use the Ultra Instinct Sign at will. Strong as he is, Goku's chances of defeating Broly are still very low.
Jiren is the only mortal being to be above a God of destruction, meaning it is almost impossible for the Hakai to affect him. His unfazed reaction during Topo's fight against Vegeta could indicate that he was not impressed with the destructive capabilities of such a technique.
Jiren was able to survive an assault from Mastered Ultra Instinct Goku, putting him on a truly elite status within Dragon Ball Super and DB in general. There's no question that with this level of strength, Jiren could resist diluted Hakai energy.
In Dragon Ball Z: Lord Slug, after Piccolo transfers his energy to Goku, Goku uses the Kaio-ken x100 to rip a hole through the giant Lord Slug. In Dragon Ball Z: Cooler's Revenge, during Goku and Cooler's initial fight, Goku seemingly uses the Kaio-ken (though unnoticeable, as it was in "Bold and Fearless").
While Goku and Jiren were relatively evenly matched during the Tournament of Power, and once MUI came into play, Goku will eventually beat Jiren with ease. The Moro arc already saw Goku prioritizing his control over MUI, a critical factor in Goku's survival versus Jiren.
As the Omni-King himself, Zeno is most likely completely impervious to Hakai techniques no matter who uses them. He reigns above the Gods of Destruction and is undoubtedly stronger than them, making him impervious to their Hakai techniques as a result.
Beerus is one of the strongest Gods of Destruction in all of the universes and there is no evidence to suggest that he might not be stronger than Ultra Instinct Goku and Jiren. With his Destructor Energy, he is almost unbeatable.
Also a God of Destruction, Beerus has access to techniques against which UI provides no benefit. Not only could Beerus easily defeat Ultra Instinct Goku, but he could do so instantly should he desire, a feat no one else on this list can achieve.
Goku has become much stronger, but not strong enough to take down Beerus yet.
Hercules is the Olympian God of Strength, and he might be one of the unique ones on this list capable enough of matching and overpowering Ultra Instinct Goku in terms of pure strength. Being a Half-God, Hercules is nigh-omnipotent and invulnerable to almost anything.
1 Autonomous Ultra Instinct
Autonomous Ultra Instinct is an incredible transformation, allowing Goku to become a natural fighter whose instincts were honed to such a massive extent that he didn't even need to think twice before engaging in battle.
Characters such as Beerus can make use of this ability, but Vegeta is the only one who has access to the transformation of Ultra Ego. This is very much like Ultra Instinct which can be utilized by a few characters in the story already but the transformation itself can only be accessed by Goku.
While some may argue that the Saiyans were not using their full strength when they clashed with Frieza, that theory is not entirely credible as Monaito's healing powers had improved to the point where he could heal someone back to their full strength. BLACK FRIEZA DEFEATS GOKU AND VEGETA!
And this is where the most powerful part of episode 84 of Dragon Ball Super comes in, which you can now watch for free through this link. For the first time, Goku and Vegeta combine Ultra Instinct and Ultra Ego to fight together.
While fans will debate whether Vegito or Gogeta is stronger, they are both exceptionally powerful. However, both Fusion methods have specific requirements and drawbacks that make them incompatible with Ultra Instinct and Ultra Ego, meaning that Vegito/Gogeta will never make an appearance again.