Right, since the eaglets are already hatched, this egg is probably toast.

Presumably then this egg will take 27-28 days to hatch, which is likely too long for the eagles to put up with. They will likely presume the egg to be non-viable and chuck it.

It depends. Duck-like birds and chicken-like birds are highly precocial, meaning that the young can walk very early, can forage with help very early, etc. Eagles generally are highly altricial, meaning that the young are very helpless for a long time. There may be only a handful of the 10,000+ bird species on the planet Earth that are more altricial than the Bald Eagle and its closely related siblings species of Ern, Fish Eagle, etc. In order for this particular arrangement to work there would have to be a lot of compromise.

There are two reasons this could possibly work, and several it may not.

In favor of it working:

1) Eagles are very caring of their young and for a long time, and these eagles have other chicks. So all the cues that may cause the eagles to try and try to care for their young may be maintained, overriding the instinct to eat a duck.

2) The duck will not need much care anyway, other than keeping predators away, so the Eagles can be bing scary but otherwise incompetant caretakers and that just could work.

Reasons against it working, short version:

1) The duck will not stay in the nest and may wander off, and will be hard to care for at night.

2) The cues for a parent bird to bond to the young are narrowly defined, sometimes; while the chick will bond easily to “mom and dad” the parent eagles won’t bond as easily to a young that does not give certain clues. Having said that, this instinct in an eagle will be less developed than in many song birds because the cues evolve in cases where birds parasitize each other and nobody parasitizes an eagle.

3) The egg may not even incubate because there is proper way to incubate each kind of egg and the Eagles probably don’t know how to do this.

4) Eagle eggs probably take a very short time to hatch compared to duck eggs; there is a good chance the eagles will eventually figure that the duck egg is not going to hatch and they’ll chuck it or eat it.

5) The duck’s siblings, either while the duck is still an egg or afterwards, will want to kill it or dump it from the nest… they will want to do this to each other, in fact. The duck will have no anti-siblicide mechanisms in place because ducks don’t do this.