No. Eraserhead(aka Aizawa) can only erase the quirks of the people he can see, he can't see Hagakure(invisible girl) so he can't disable her quirk.
4) Toru Hagakure, Invisibility
Being a Mutant-type Quirk that even Hagakure can't control, Aizawa's Erasure won't do a thing to this incredibly unique Quirk.
During the "U.A. traitor" arc, however, Toru was hit by Yuga Aoyama's Navel Laser attack, which heated her body enough that part of Invisible Girl's face became briefly visible.
No; Toru Hagakure's quirk (Invisibility) is a mutant-type quirk, also called heteromorphic, meaning they are part of the user's physical body (like Tenya Iida's Engine or Tsuyu Asui's Frog). Shota Aizawa's quirk Erasure is ineffective against this type of quirk users. However, he can still hold his own against them.
Invisibility is permanently active and cannot be switched off. However, refracting light from Toru's body can reveal her true appearance, but only briefly.
And since Hagakure is invisible, he can't see her. Aizawa's quirk can't erase heteromorphic quirks - quirks that permanently mutate your body (like Ojiro's Tail). And from what is known, Hagakure's invisibility is also a heteromorphic type.
Deku prepared for the Laser, but Hagakure intercepted it. She wass able to refract it into a nearby tree, though her gloves do get singed. As the smoke clears, her body shimmered and her features were briefly visible.
So, Hagakure's quirk does not go away, just her ability to manipulate or activate it.
However, there is always the possibility that Eri could restore him back to his old self. With that said, she is not a magical problem eraser. Eri is still a small child despite her deus ex machina powers in My Hero Academia, which is why there's no other way for Aizawa to go back to normal if not for her powers.
Eraserhead is a very effective Pro Hero, and his quirk can devastate All For One from afar. Thanks to Erasure, he can nullify the quirks of other individuals, thus turning All For One into a normal human.
This, however, is a misdirection. Chapter 336, "Villain," reveals that the real traitor is Aoyama Yūga.
Toga quirk is to take on the appearance of other people but she is NOT able to utilise their quirk. And since Hagakure quirk is invisibility, in a case that Toga somehow manages to ingesting Hagakure's invisible blood, Toga will look like Hagakure but visible to our eyes!
Tsuyu uses her frog-like body to match the temperature and color of her surroundings in order to mask her presence. She does not become completely invisible, but she is still able to sneak up on her targets.
Not only would Aizawa need to lock eyes with Toru in order to erase her quirk (which is impossible, because he can't see Toru's eyes), it is also stated that Aizawa cannot erase mutant type quirks.
This one may be the hardest fact to believe: Aizawa does actually smile from time to time. Actually, when he really lets go he can have a complete grin on his face. Though usually, that's because one of his students surprised him or succeeded in some way. More proof that he cares for them more than he lets on.
Binding Cloth: The cloth on Aizawa is used for combat, made of carbon nanofibers and a special metal alloy. Using his Binding Cloth, he's earned a 6/5 in Technique; an S rank. He is very agile, to the point of being inhuman, and uses his cloth to restrain opponents, working well with his quirk.
As Eraserhead says when he's escorting Deku to Nighteye's room, Eri's Quirk is not under control and is likely to destroy someone rather than heal them, which is why he says "We cannot depend on her Quirk" - specifically, they can't make use of it to save Nighteye.
Eri's Rewind Quirk also requires a huge stockpile of energy, and even if Neito copies it, he wouldn't borrow the saved-up energy, thus her Quirk is also a blank.
Aizawa can't erase mutant class quirks. Unlike emitter and transformation class quirks, most mutant class quirks don't require the quirk megastructure to affect them for every instance of quirk use. They can simply use the abilities inherent to their bodies.
No, he cannot erase physical attributes of one's quirk (Mutation-type quirks being the biggest example).
To reiterate, Aizawa did not lose his Quirk completely. However, it is effectively lost as he can no longer use it in battle.
His quirk, Erasure, can only erase one quirk on any select individual, but he can erase multiple quirks if they are on different people, but only if they're on different people. So it would be impossible for Aizawa to erase all of his quirks, maybe one, but that's it.
The "U.A. Traitor" is revealed to be Yuga Aoyama. He was born Quirkless, and with his parents both coming from wealthy backgrounds, they made a deal with All For One to give him his Navel Laser Quirk in a desperate move to grant their son a happy, successful life.
Since one of the earliest favors All for One is shown doing is taking someone's quirk away, it's possible that Toru simply wants to get rid of her invisibility quirk and live a normal life.
Katsuki Bakugo (Japanese: 爆豪 勝己, Hepburn: Bakugō Katsuki), also known by his nickname Kacchan (かっちゃん, Katchan) and his hero name Great Explosion Murder God Dynamight (大・爆・殺・神ダイナマイト, Daibaku Kisshin Dainamaito), is a superhero and one of the main protagonists of the manga series My Hero Academia, created by Kōhei ...