Yes, but it will take a long time.
Koi fish will indeed starve to death if they are not fed for a long time, but this process usually takes a considerable amount of time, which specifically depends on the environment and the health condition of the fish.

1. The Hunger Resistance Ability of Koi Fish
Healthy koi fish can endure not eating for one to two months without starving to death.
In a natural environment, koi fish will look for food on their own, such as benthic animals, fragments of aquatic plants, and seaweed, so they are less likely to starve to death.
2. Consequences of Not Feeding for a Long Time
Even if koi fish don't starve to death immediately, not feeding them for a long time will lead to malnutrition, gradual weight loss, and an increased risk of getting sick.
In an aquarium, koi fish can't forage for themselves. If they are not fed for a long time, their bodies will become weak, and they may eventually die from getting infected with diseases.
3. Survival Limits in Extreme Situations
In extreme situations, koi fish may not starve to death until they haven't eaten for more than three months.
However, it should be noted that water quality and oxygen supply are equally important for the survival of koi fish. A poor environment will accelerate their death.
4. Feeding Suggestions
Although koi fish have the ability to resist hunger, for their healthy growth, it is recommended to feed them regularly and keep the water quality clean.
Avoid overfeeding, because koi fish are more likely to die due to deteriorated water quality or digestive problems.
Conclusion: Koi fish will starve to death if they are not fed for a long time, but this process usually takes several months. To ensure the health of koi fish, it is recommended to feed them regularly and maintain a good water quality environment.