Unlikely, for a couple of reasons -
in vitro studies, as you mentioned, are pretty limited as a lot of substances neutralize various disease in a petri dish. Unless there's a practical application that can be foreseen as having significant benefit, they usually don't go very far.
Second, in order to prove merit in vivo, it would be necessary to have controls - usually in the form of a double-blind study. This would mean that half of the participants would be using mouthwash, and half would be using something that tasted like mouthwash, with no active ingredients, and then both sets of subjects would have to be deliberately exposed to COVID. I'm sure you can see the ethical dilemma and subject recruitment problems that would create.
Having said that, it won't hurt you if you choose to use mouthwash, so if you want to do so, there's no reason not to.
Is this Spam? Can't tell. Are you selling Listerine? Can't tell. While Listerine advertises it kills germs, it doesn't ever say what germs, and it has gone round and round with the FDA about this. For awhile, they had to take this off the label and their advertising. Then it was back. There are a lot of germs in the world, and alcohol alone kills a lot of them. That's what hand sanitizer is, if it's the right kind of alcohol and at the right percentage. It's not Vodka, which doesn't work. So the fact anything kills some germs doesn't mean it kills anything that causes disease. It might in fact kill more beneficial germs than harmful ones. If you're relying on Listerine, good luck to you. I use natural mouthwash myself, which also will show if you look through a microscope that it kills bacteria. But it certainly won't kill anything as serious as the flu or covid. Of course it gets in the nasal passage, that's why the test swabs the nasal passage. That's a given. But once you've been exposed, if it gets deep in the nasal passage, you've got the disease. If it's only shallowly there, you probably won't get it or you won't get a bad case, though you still can pass it on to others. So the Listerine isn't getting to where it belongs unless you're using it against instructions and unsafely. It also has ingredients in it that are toxic, which is why I use a natural product. You haven't gotten the flu because your immune system has worked well or you haven't been exposed to it. I don't use Listerine and I haven't had the flu, either. What does that prove? A ton of things in this world are anti-bacterial to some extent or other. Few are anti-viral. You would do better to just use saltwater at the appropriate concentration for any purpose cleaning the nose gives you. It has no additives. As for the mask thing, nobody ever said masks wouldn't help. They said masks were in short supply and were more needed by physicians than by the rest of us. As the disease progressed and spread uncontrollably, the advice changed quickly, and we were all told to wear a mask, but to make our own so docs would still have all the masks that actually work really well. For the rest of us, our masks work some and social distancing is the rest of the picture. Masks alone without distancing has never been the advice. At this point, most people could obtain some kind of the best masks out there, but most of us are still using cloth masks so the docs won't run out. They can't social distance. Peace.