Oh, yes, they do grieve terribly. Bimmer was grief stricken when we lost our Buffy. He didn't begin to recover until we brought Shiva home. He hadn't had an appetite, or played or even responded happily to attention. Even his favorite activity in the universe - running in the pasture with the jeep while Charlie counts the cows in the evening - failed to get any kind of happy response from him; it may have actually depressed him more because he and Buffy always went together.
About a week after we brought Shiva home he started playing with her a little bit, by two weeks he was playing hard with her and starting to train her. When we brought Kharma home it was the same process, and after about a month and a half he started to treat Kharma in some of the same ways he did Buffy.
But he still misses Buffy. Sometimes, if he's sleeping and one of us mentions Buffy's name, he'll jump up fully alert and look around, then sigh softly and lay his head back down and close his eyes, making soft little crooning noises until he falls back asleep. And even now, he's much more serious and never plays and cavorts as much as he and Buffy did together.