The word "monster" is a judgement that discards sympathy, so in a literal sense a sympathetic monster is a contradiction in terms. To feel sympathy, you have to see the humanity and that makes it a monster no more. Also, to see a "monster" in that way is somewhat antithetical to a horror designation. Horror plays upon fear, and fear fades when the humanity in the beast is shown.
True, although it's interesting to note understanding someone's thought processes could lead to showing one could end up their themselves. That's terrifying from a psychological perspective, by showing how vulnerable we are to doing horrific actions ourselves. Granted, that's empathy, which is different, but similar enough to impact this question.
Sometimes it works, sometimes it makes the character less scary. Carrie was sympathetic and that made it a great movie. She might have been scarier as a sociopath, but the movie wouldn't have been as good in my opinion. But, sometimes adding too much background ruins the monster. Rob Zombie's Michael Myers with an abusive childhood is less scary than the original Michael Myers who had a normal, middle class childhood. The fact that we don't understand why he killed his sister is what made him scary.
It depends on how well the "victim's" point of view is depicted. It might even increase the horror when the reader goes into a scene feeling a degree of sympathy for the "monster" and then (say) a mother watches it rip the arms and legs off of her child. "But it is so sad! How could it possibly ... OMG!"
Of course monsters can be sympatric. They are always feared by humans and they can't control their own nature. Frankenstein and the wolf man are good examples.
