Nope.
They can pretend to, of course, and use the language of grief, but if you can't feel the cold bottomless pit that has bored through your gut then you aren't really grieving.
How do you know that they don’t? And conversely, how do you know any other human than yourself do?
Do whales grieve?
How do you know that they don’t? And conversely, how do you know any other human than yourself do?