No, don't let her keep the eggs. Nothing will hatch from her eggs anyways, and it's not good to let hens brood when you no nothing will come of it. Even if she had a had a male mate, or flock sisters, she'd still be laying, and wouldn't necessarily go broody.
Do you plan on getting anymore ducks? They're flock animals, and while they can enjoy human and other animal companionship, they are happiest being with their own kind.
You can and should be collecting the eggs daily, and they are edible (and delicious! Duck eggs are great for baked goods). The only reason you would not want to collect eggs is for the hopes that she will go broody, which I don't think is what you want.
It sounds like you're just finding hidden nests. Ducks are only capable of laying one egg a day, very rarely two, and they don't lay every single day. Since she is laying eggs she is not broody. I'm not sure why you are concerned that she is laying eggs? That's what healthy ducks do.
Have you...