Absolutely! My 13-year-old Himalayan, Kirchen, was very depressed for a while after her sister Kepler died last year. We had to put Kepler to sleep when she became very sick with lymphoma, a very aggressive cancer. She didn't want to eat much or play, and she just clung to my husband and I. Kepler and Kirchen were very close in age and looked very much alike. We have another cat named Skye who didn't want to spend much time in the house afterwards. Since then, we got a Siamese kitten named Schrodinger who is now 9 months old, and he keeps them on their toes-- he doesn't give them time to mope, LOL! Schrodie was a kitten that one of our clients found in her bushes, and being a "Meezer" kitten, he just wants to play all the time!
If you can't pinpoint a reason why your cat would be emotionally depressed, it's possible that he's sick. If he's not eating well, or otherwise isn't acting right, take him to a vet to be sure that he isn't physically sick. Cats can't tell us if they don't feel well, and being cats they wouldn't tell us even if they could. Cats hide illness as a protective measure-- a sick cat in the wild is an easy mark for an enemy. Have him checked out. Better safe than sorry!