Yes, there have been many times where animals die of heartbreak. You just need to be there to mourn with them so they can feel the love still there. My rabbit and my aunt's dog were very close and after my rabbit died there was a period of time where her dog was depressed.
We had two puppies (not related) and they were the best of friends, always play fighting and such, I'm waiting for Max to realize that his friend is no longer with us. I do believe they get depressed, it's the same as a human losing someone close
I am so sorry for your loss. My heart goes out to you and your family. We lost our dog in January. He died in our arms at home, surrounded by those that loved him. We also have another dog, and we allowed her to sniff his body, and his mouth once he was gone. She mourned, but she didn't mourn as badly as we thought she would, and I truly think that that is because we allowed her to spend a few minutes with him, just checking him out. Keep an eye out for certain symptoms. That would be lack of appetite, sleeping all the time, not playful, for fur that falls out, out of season. If you notice any of these, and it looks like maybe your dog is not going to get better, take 'em to the vet, and they should be able to help with that.