Personally I'd put at least some eggs under the hen. I often collect eggs for a week after she goes broody before I start them. I can't give guarantees with living animals, anything can happen, but I've never had one quit before she hatched the eggs. Before a hen starts laying eggs she puts on a lot of extra fat. This fat is mostly what she lives on while broody so she can stay on the nest instead of needing to be out looking for food and water. A hen will lose weight while broody but it is fat put there for that purpose. That does not mean it is unhealthy. I have no qualms with one being on the nest over five weeks. If it is going to be longer than five weeks i break them.
Sometimes eggs get shaken up during shipping but not always. I've had a100% hatch with shipped eggs, I had a 16% hatch with shipped eggs. You can't tell what will happen with shipped eggs.
If you don't have an incubator and will just toss them I'd absolutely give them to the hen. Or maybe candle them, give the best two or three to the hen and incubate the rest. Then give any that hatch to the hen to raise.