Both Koi and Goldfish will eat their eggs if given the chance, to them it's just an extra food source.
Firstly it is not a good idea to try to keep koi in a pool (pond) designed for goldfish. Many pond keepers want a combination of pond plants, lillies, oxygenators and marginals to decorate the pond and keep the water quality in good balance. To this can be added a selection of goldfish, fancy goldfish (fantails etc.) and shubunkins.
Koi are fish that are capable of growing to up to a metre in length and would in a very short space of time decimate a pond of it's plant life by ripping it up and eating much of it, leading to the pond losing it's ecological balance and becoming a horrible green stagnant eyesore.
From the breeding point of view if the pond is well stocked with oxygenators and floating plants (water chesnut) goldfish will chase the females en masse into the plants to release her eggs and the males eject their milt (sperm) to fertilise them.
They will also try to eat them but as a general rule if the pond is well planted some will survive to hatch and hide in the plants until they are large enough to survive.
Many hobbyists involved in the showing of fish will transfer the plants, with eggs attached, to a nursery pond to hatch so they can rear a high porportion of the spawning.