No, Karasuno High School does not win nationals in the Haikyu anime. Although they have participated in the Spring Tournament multiple times, they have never emerged as the champions [2]. However, they have come close to victory and have made significant progress throughout the series.
Here is a breakdown of Karasuno's journey in the anime:
Karasuno's first major achievement is reaching the Spring Tournament after defeating their rivals, Nekoma High School, in the "Battle at the Garbage Dump" [2].
In the Spring Tournament, Karasuno faces Kamomedai High School but unfortunately loses the match [2].
In their third year, Karasuno reaches the semifinals of the Spring Tournament and places third overall after losing to Itachiyama Institute [2].
While Karasuno does not win nationals in the anime, their efforts and hard work help them regain their status as a powerhouse school in the volleyball world [2]. It is possible that in future spin-offs or continuations of the series, Karasuno could have the opportunity to win nationals.
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