can a broody lay eggs

[chickenshiha]

Today my hen finally went broody she was sitting on 2 eggs so I put her by her self in another coop I went to check on her a little while ago and I found 3 eggs her coop is shut and the chickens can't get to her she is still sitting and it's get dark so I'm sure she's broody

 

[aart]

Yes, they can lay while going broody.
But once they sit on those egg for 3 days and 3 nights(sign that they are truly broody) they will not lay.