Absolutely!!! A few years back, I had to have oral surgery. When my husband brought me home, needless to say I was really out there. My Rottie, who is very, very smart, and probably out of all my dogs, she is the one who stays by me all the time. Possibly because I rescued her, who knows. But that day when I came home, she immediately came by me, I was lying on the couch, and at first she jumped on the couch, and did not leave me for awhile. That became quite uncomfortable, and again, I think she knew, so she ended up on the floor right by me, and stayed there all day. My husband always said he had never seen anything like this in a pet. Also, my mom who I cared for, she has Alzheimer's and now in a Home, well, again, not only my Rottie, but all of my dogs were constant companions for my mom, no matter where she was in the house, a pet was always by her side. So to answer your ?, YES, pets do know when their owners are sick, upset, depressed, or just not right. Again, who says animals are dumb.
Debi