Will a princess parrot and budgie share a cage happily?

Budgies are territorial and may nip at a Princess Parrot, Princess Parrots are quiet timid birds. In response to a budgie nipping at them their bigger beak could do some damage to a budgie. I have read that due to Cockatiels having a calm nature like Princess Parrots that they can be housed together, but don't house females together as this can prompt egg laying and then you have a whole new set of health issues such as a egg bound bird to deal with.