There is absolutely situations where people will survive this. I have no doubt that there there will be damage done to the world, and as the person building the world, it will be up to you to define the scope of the damage you want.
I would expect a good number of people that live alone and have enough resources to survive for two weeks to just quarantine themselves in their domiciles and avoid dealing with anybody. They will not be particularly violent unless provoked.
Children will take a hard hit as parents will hate them and have the potential power to take that hate out on the children. Expect a generation of traumatized children depending on the actions taken by the parents.
Expect at least a few assassinations of world leaders as people no longer fear the secret service, military, or police enough to stop them from doing it. A sharp increase in suicides are also inevitable as people as the suicidal lose their fear of killing themselves.
The biggest dials of mayhem are people going on bloody rampages and world powers bombing each other in their period of irrational virus-induced hate.
Overall, the world will go on but be forever changed by the event, and then the aliens will land ... a convenient target.
What is Hate?
Hate, as defined in the dictionary is to feel intense dislike for or a strong aversion towards something or someone.
The important thing here is that humans are not a cookie-cutter species. We all hate in different ways, as has been stated. And just as we all hate in different ways, we will react to what we hate in different ways. It just depends on what we are hating, our options for dealing with it, the tools at our disposal, and what we are willing to do as a person.
How Will You Hurt Me?
However, this is a virus. It will have to be ... programmed ... for a lack of a better word, to target something concrete. It might have the overall effect of humans hating each other for a fortnight and the loss of fear, but how is that achieved?
- Does it mess with our natural pheromones so that instead of wanting to be near humans, we develop an aversion to them? Powerful, and not everybody and live with this for the two weeks.
- Does it merely amplifies what is already there so that even a little annoyance can blossom into a full-on hate? This means we will not hate people in the same ways, and as such our responses to this will be different.
The biggest question here is if the virus does anything else, either as a main effect or a side effect? Will this virus encourage us hapless humans to a particular action or remove our inhibitions towards certain less savory actions?
Something to keep note: There are people that do not fear the consequences of their actions -- they know them, acknoledge them, and choose not to do the actions that cause those consequences. Because it is not a fear, it will not be suppressed during the virus' run.
The assumption is that physical violence will be the first reaction to a person you hate -- It might be if you can't really get away from them. Lacking fear means that a person might be more willing to confront another, but nothing about the virus eliminates rational thinking entirely. Fear of getting caught and arrested is a thing that will be suppressed, but if murder and maiming isn't really in a person's line of thought, they still won't do it unless the virus prompts them to it.
But there is also character assassination as well. Those that have dirt on somebody might hate them enough to release the dirt and let other angrier people deal with the person through more physical means. The will lack the fear of the retaliation that will be brought down on them so one of the main reasons holding them back will be negated.
You Hurt Me
On dispersal, the virus is released throughout the planet. Assuming a 99.99% initial infection rate, the world will turn in itself within the next day or so. Note I am going to presume roughly 700,000 people unreachable for assorted reasons from isolated environments to unknown immunity.
Some people, if they hate enough will absolutely go on a rampage to deal with all these hated humans. In places with easy firearms, this can get very lethal, very fast -- we see this with mass shootings already. But it is the other effects that are going to be the most insidious on our world.
Work and productivity will practically grind to a halt for those two weeks. In places with low worker protections, people will be arbitrarily fired because they are hated and that hatred will outweigh the fact that they might be a good worker. Deliveries may not be made as shipper and consignee will not want to deal with each other, not even going into account the stress that working for a shipping company can create when employees and management tolerate and like each other (or at least understand and accept).
There are also armed groups of people in close qarters to each other -- police and military. Some of them are already willing to resort to escalation before deescalation so if the police hate each other enough, there is a possibility that those organizations implode on themselves. They may also go on a power trip amongst the civilians unafraid of reprisals from their superiors.
Consider that managers will hate their employees. Any firing of the rank and file might prompt those people to go public with a lot of dirty laundry that these organizations never wanted to see exposed. Others might use their power on the populace, forever destroying their credibility as a respectable organization.
Politicians, world leaders, and celebrities are in a particularly precarious position. Their bodygards will hate them due to the virus so there is likely no help on that front. Considering that people that hate these kinds of people now have been known to send hate speech to them over social media semi-anonymously already, how long in this fortnight before somebody decides to try to remove them physically so they don't have to look at them anymore?
The biggest worry is the world leader that can launch all the dangerous weapons, is willing to do it, and is neither afraid not caring of the retaliation.
Then there is the after-effects of the virus on humanity and the terrestrial world.
We already know that Covid-19 can reinfect people months later -- what happens when this virus manifests months later in random suseptable people? We will be dealing with random bouts of irrational hate and fearlessness for years to decades. Does this start to fall into a seasonal pattern like influenza and the cold, or are we going to get intermittent pandemics that cause ripples of chaos and mayhem?
Can this transmit from humans to animals? When this virus crosses the species barrier (and there is a good chance it might), is the hate still keyed to humans or will it be keyed to their own biology? Will the fear suppression work to supress animal insticts to avoid certain things? A wave of fearless geese that hate humanity is a rather terrifying thing considering many of them are urban and are already unpleasant when even mildly provoked.
Then there is the cleanup after the fatigue phase -- dirty laundry has been aired, many will be dead, and there is a month of shutdowns and neglect to clean up over. It will not be pretty, and there will be a drive to understand what happened, to blame somebody or something for the mass disruption to the world order. Humans can hold a grudge, and then the aliens arrive ...
While a four week plague, I suspect that we as a world will feel it for a lot longer than that.