Can parralets live in a cage with parrakeets?

I have babies in the nest in a very tall cage. They are at the top of the cage. Will they be ok when they come out? I can hear them, but they are in a cane nest, and I can't see them. I am not even sure how old they are, as I thought my hen was barren. She had been in the box for months, and then suddenly we heard cheeping.

I want to get another parralet and keep it in a separate cage, but my husband is thinking they could all live together. Good idea?