They'll love that.
Budgies are very gregarious. In the wild they nest in tree hollows, but don't use nesting material. Breeders use oblong boxes, with a 'pop' hole at one end (in the long side wall), and a hollow in the thick wooden floor at t'other, which is where the eggs are laid. The hen birds incubate; the males just hang around, preening!
You might add a couple of nest boxes to your flight cage, and you'll probably have success (although chick rearing by hand is quite another matter). We had an incubator made from a small coffee tin, and did successfully rear a few abandoned eggs, but it's really hard, especially when they are tiny hatchlings. But if you have one experienced hen, the others will learn from her. But like chickens, though, there really is a pecking order, and I've known them draw blood. Peace seems to break out quickly though.
The laying hens need a good source of calcium - cuttlefish bone is the traditional choice. For all the birds, too, it minimises the damage they do to woodwork (their beaks need to be abraded away, otherwise they can grow too long, like toenails, which is one reason they like to chew).
It's tempting to have an external flight cage also (they get better exercise), BUT if you build one, you need two layers of mesh, separated by about 2-3 inches. This is to stop predators (small hawks and corvids mostly) from being able to physically reach the birds. Also don't have feeders in the external cage, as that attracts rats and mice, which are great at chewing through anything wooden to get at food. We once lost six birds in one day to a jay, which was my fault! I didn't get them in for the night (into the indoor flight cage), as being summer they were happy to roost on the wire outside. In the morning we discovered the carnage - the jay had skewered them either at dusk or in the early morning (it had previously been seen but chased off).
All that said, your flight cage brings back very happy memories. It was a great childhood learning experience, and we had a flock of around 20-30 (at the peak), most of which we'd bred. And I still love the chattering, whenever I hear it!
