Very few domestic chickens lay a clutch of eggs and then start to sit on them. A few breeds or individuals might, but most will not. She will lay eggs for an undermined amount of time. It will not matter if you pick them or not. A few people who desire the hens to brood will leave a small group of eggs out to encourage the hen to sit, but they will not sit on eggs unless their hormones "tell" them to. Most domestic chickens never go broody. What type of hen do you have?