They usually do
But if you have other ducks, they might lay in her nest, so it's a good idea to mark the eggs she starts with so you can take out any new ones that appear. And if she's laying new eggs, which it sounds like she is, you'll want to take those too because she won't stay on the nest to hatch them after the first eggs hatch. My pekin has gone broody twice this year, so they definitely do go broody, but it's a rare trait in pekins. You can tell if they are going bad by candling them - dead embryos are very apparent compared to their live counterparts. Any that die you take from the nest and toss out. Here is a candling chart for you so you can see what you're looking for: