Yes, every dog I've had the pleasure of having has been that way.
My two dogs I have now are very much in tune with their dad's feelings. If I'm feeling hyper and great, they do the same. When I'm mad or upset, they lay next to me and just relax. A good way to check or stimulate this is to play a little rough with your baby and pretend you got hurt by them.. cover your face and whine and cry and see how they react. When I do this my dogs go nuts, licking my face and whining..
I lost a VERY close friend a few months ago. After I got the phone call and just sat on the couch sobbing, both babies ran up to me and just started licking my face and looking at me as if to say "Dad.. It's OK.. We're here with you"...and they sat with me all night. Slept with me in bed and even into the next day they were so very close.. They'd even look at my wife and whine as if to say "Mom.. Look at dad..He needs us.."
I have felt so much closer with them since that day..(Don't get me wrong, before that day these kids were my life, still are) They knew I was hurt and they were so in tune with what my heart felt and it effected them emotionally as well. To me that's HUGE.. To me it's so crazy how a dog knows how to read and react to their parent's emotions.. Mindblowing in such a special way. I love these kids..