If the tank were empty and it was left to cure at least 48 hours it would work but it would probably end up being a hassle for cleaning. However, there are other options. You can go get craft mesh from your local craft store and use it as a shield.
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Or if your just occasionally flare at each other just let things be. As long as you have some plants for cover in the tank. The fish will soon learn that they can't get to each other and just ignore each other and once in awhile when they feel like some entertainment they will swim over to where the other betta is and flare and race the tank. This process of getting used to each takes about a week or two. Have you noticed bettas in petstores generally ignore each once they get used to the sight of each other?
Some people feel there is some wrong with this but I have found most bettas like to be able to see another fish the realize the other fish has glass wall too and is not a real threat. I've seen my fish actually act depressed if the fish the seemed to "like" passes away. Seeing other fish gives them something to do besides stare at nothing all day inside a glass box. I notice my bettas even watch my nearby cichlid sometimes in another tank.
So you can go get a divider screen or give your fish some time to get used to the sight of each other and you will enjoy watching them interact occasionally and they will have something to do with themselves when they feel like it.
There are exceptions to this practice. Some bettas are excessively aggressive and just don't stop flaring and they might benefit from a divider. The other sign your betta is not liking the interaction is that they spend lots of time hiding in location that appear to be as far from the fish next them is they spend time in the tank in corners on the bottom any place the other fish is not. If you put up divider and notice the fish is more active moving to all parts of the tank then that is another fish that will do better with a divider.
