I'm not going to get into a "Yes" or "No" because... seriously?
Let's look at what horror is and why it works though. The most popular horror stories are the ones that have been ground in reality in some form, rooted to "What if" and "Could it happen?". The earliest examples you can point to involve the works of Alfred Hitchcock. The attack of animals against humans en mass in a way we can't defend against, a man who has his ability to connect between who he is, and an important figure in his life, the story of a man who struggles with the knowledge of a neighbor who is violent and able to hide his activities. Hitchcock worked because these were themes that people could see happening, and could genuinely be concerned with happening. This was an era when there was so much unknown detail in medicine, mental disorder and during troubling periods of people bringing about fear of murder or harm.
This can further apply to something like the Texas Chainsaw Massacre, a movie heavily based on a real event, again dealing with mental issues. And everything was framed as to make it much more real, and brought a fear of strangers and the ill.
When we get to the 70's and 80's, we started looking at space, computers. Nobody was sure how computers could advance, if they could become so smart that they would turn against us. Novels like "I have no Mouth and I Must Scream", movies like "2001: A Space Odyssey" and "Alien", they were the fear of unknown, would could be in space and what we could have created.
Now, as far as the asked topic in question, violence against one another is always a possibility. It's looked at from a very, very similar perspective in every situation in media, generally sexual violence against women, in rare instance by demon or monster (See the Bruce Campbell films, the Evil Dead series as one example). Rarely does movie or film focus accurately on the situation in a way to actually pass that intent to horrify or show brutality of it towards the victim, instead either turning the situation into a means of revenge/vengeance, killing the victim soon after or by having them simply "get over it" in a brief period, when in actuality the event causes a large amount of various harmful effects physically, emotionally and psychologically. One example I would point to as being a rarely seen example are two characters from Fallout: New Vegas and the effects that it has on the characters around them (Granted, being a videogame you "solve" the problem fairly easily, so it's still not the most realistic situation). Another thing I would point to is actually the film "Gone Girl", where the premise of multiple sexual assaults is turned on it's head, the perceived victim for the entire film in reality orchestrating the situations for her own benefit and taking advantage of the situations for her own benefits, no matter how brutal the means or methods (And men, should you watch it, will probably be fairly horrified from sex for a while.)
In any case, the eventual answer is that as a theme of horror it's an item that can be used to some effect, but you would not put zombies in every horror story. You would not put zombies in every horror story, nor aliens, sentient robots, chainsaws, cannibals, Hannibal Lector, Genghis Khan, evil Jellyfish, shapeshifting clowns, tentacles, octopus, lasers, flamethrowers, robots, Steven King, werewolves, skin-suits, flesh-covered books, witches, dark magic, Satan, occultists, spiders, cockroaches, birds, strangers, or fear itself, in every story. They might try to use it, but so rarely will they treat it in a way that has any real impact and doesn't take away from the seriousness of the issue.