I believe it's more stressful on the owner than it is the bird. At least it was for me. I went on vacation with my wife to the Virgin Islands to visit family and was gone for two weeks. I left my Senegal Parrot with my nephew. It killed me to leave her. I wondered how she would react when I got back and if she would even remember me. Weeeellllll, let me tell you, as soon as I walked in and she saw me, she stated making kissy face sounds and when I opened up her cage, she climbed up on me and when directly to my face giving me kisses for a good 15 minutes.
We ate supper before loading her in her pet carrier and she stayed on my shoulder the whole time.
But to me, it's always best to take your pet with you if you have the opportunity. But if not, they will be fine as long as you trust the person or people who will be taking care of them.