Things would mostly work.
Realize that a modern aircraft carrier would only have enough modern jet fuel as she holds, after that unless the Navy is in the habit of putting how-to-refine-jet-fuel texts that are detailed enough to be of quick use to 1940s refiners the actual impact the ship could have is less in your face than for her tactical ability and historical knowledge. As for technical knowledge of her crew, think that one novel where a small US town ends up in Europe centuries ago for comparison ... only in spades.
Under those circumstances, the war will almost certainly start to go differently even if she never mounts an airstrike, her most valuable aircraft will not be the fighters and bombers but her surveillance and ASW craft.
The 1940s USN could absorb the ship and otherwise fly conventional 1940s attack planes from them early in the war when they were desperate for carriers. That said later on, and not THAT much later, the smart move would be to hold in reserve the valuable ship and her even more valuable crew to quickstart a technological revolution back home.
And not just for suddenly giving the US the whole basis for integrated circuits and advanced concepts of programming that otherwise took decades after the movie to earn.
There an SF story called “Hawk among the Sparrows” which is a similar premise - a modern military jet goes back in time to the First World War.
It’s interesting because there’s a lot of unforseen problems using the modern weapon in the past, one of which the airspeed is so fast the weapons are kind of pointless.
“after that unless the Navy is in the habit of putting how-to-refine-jet-fuel texts that are detailed enough to be of quick use to 1940s”
Basically Kerosene
“As for technical knowledge of her crew, think that one novel where a small US town ends up in Europe centuries ago for comparison ... only in spades.”
Realize that a modern aircraft carrier would only have enough modern jet fuel as she holds