It depends a lot on the type, temperament and age of the parrot. Are you putting them both in the same cage? Often that will result in them bonding with each other..... if kept in separate cages, but in the same room then they should still stay bonded to you. Still depends on the parrot however..... I have a 16 year old Quaker parrot, he has never liked another bird and will not tolerate another bird in HIS cage. He is pretty much set in his ways.
They will be fine as long as they are in different cages. They do need to be handled daily and need lots of toys. Toys with wood pieces that they can destroy are the best. It will help keep them busy when you aren't home and will satisfy their need to "forage," even though they have plenty of food in their bowls.