Yes they can. Even without projecting emotions. We all know that reptiles don't deal with change well. the death of someone in the household would be a huge change. There has been many documented cases of reptiles getting sick from stress after losing an owner.
and in my own reptiles, I've unfortunately seen it a few times. First time I got dragons, I bought 2, Dante and Isis. Isis died shortly after I got her, and Dante was never the same. Isis was very outgoing, and Dante very reserved. But she kinda brought him out of his shell. there were many things he wouldn't do unless she did them first. When she died, he was never the same.
With the ones I have now, I originally had 3. I had them all in 1 tank with a divider down the middle, Astarte and Bane in half, Sokar on the other side. When my husband came home and discovered Sokar was dead, the other two were sleeping right up against the divider, Astarte was almost exactly opposite where Sokar was lying. They both were dark and not very active for weeks afterwards. They really they've only recently began acting like their old selves again. Astarte was the most affected. For like a month my beautiful orange dragon was brown. She looked like she had been playing in the mud. And her beard would go black for short moments throughout the day. Her next shed took forever to come off. I was really worried about her for a while.