I don't have an Eglu but you will need to make sure the chicks can get to food and water, and if there is a ramp up to the coop part, make sure they don't fall off the ramp and get stuck outside the coop while mama went inside. Looking at pics of it online, it appears that it is going to be well nigh impossible for new chicks to keep up with mama if she goes in and out of the coop.
So you may wish to put your hen and chicks after they hatch, in a weatherproof dog crate inside the run area (safe from predators) with food and water- just an idea. If you will supervise her you could let her out once a day for exercise and she can take her chicks onto the ground for a bit. But if she goes up into the coop area they will have no mama for awhile- they could be killed by other hens.
But I don't know what kinds of predators you have. I don't know...a dog crate may let in snakes or other predators???
I like a chick-n-hutch for my broodies (in the past I have used them).
I'm thinking about buying a wooden nest box to put on the floor of the coop so the hen can take the chicks there... Because the chicks with need to be hand placed in the Eglu for a few weeks for it to work... Which I am not doing!