I am not an expert.
That said, I think you can add layers to your 13 week old flock. I mean they will be almost 18 weeks and maybe starting to lay (depending on breed) by the time the new birds are out of quarantine (30 days in a coop at least 15 yards from your flock). I would make sure the three new birds are all friends and great together before adding them to the new flock, as pecking order can be hard and at least the three new birds would have one another! Them laying shouldn't be an issue!
That said, I think you can add layers to your 13 week old flock. I mean they will be almost 18 weeks and maybe starting to lay (depending on breed) by the time the new birds are out of quarantine (30 days in a coop at least 15 yards from your flock). I would make sure the three new birds are all friends and great together before adding them to the new flock, as pecking order can be hard and at least the three new birds would have one another! Them laying shouldn't be an issue!