As you can probably tell by my screen name, I had to reply to this post!
Definitely YES - animals are very calming, and multiple scientific studies have even documented this fact.
I have two certified therapy dogs, and every time I take them to visit patients in the hospital, I witness the amazing healing powers that animals possess. We often visit the psychiatric floor, and time after time, I watch people calm down and become more grounded after spending time with the dogs.
In my own life, my dogs and cats have been my best therapists. The animals are there for us, no matter what. As the saying goes, "They ask no questions and pass no criticisms."
I've been visiting hospitals with my dogs for three years now, and it's very clear to me that the dogs often communicate with people on a very deep level. During last week's visit to the hospital, we met an elderly woman, and she was deeply agitated. I lifted my dog up for her to pet, and when my dog's eyes met the patient's eyes, there was an instant spark. The patient calmed down and intently watched and petted my dog. The nurse later commented that no medication had been able to calm her down that much.
So, without a shadow of a doubt, I firmly believe that animals can calm us down tremendously!
One of my favorite quotes describes this perfectly:
"The best way to make friends with a dog is to talk to him. He can't talk back, but he can understand a heap more than you think he can."
"How far you go in life depends on your being tender with the young, compassionate with the aged, sympathetic with the striving and tolerant of the weak and strong. Because someday in life you will have been all of these." George Washington Carver