I doubt there is much about this specific situation, but see https://en.m.wikipedia.org/wiki/Brain_training for a broader discussion:
Scientific investigation into the effectiveness of brain training activities have concluded that they have no impact on intelligence or everyday cognitive ability, and that most programs had no peer reviewed published evidence of their efficacy.
This is not well-referenced on Wikipedia, but I think there is a very clear lesson: if someone wants to make a claim that something they offer is useful, they need to provide evidence. No one else needs to bother to show it doesn't work, and if the person trying to sell you on something doesn't bother to actually study the thing they're claiming, then they don't have any idea whether it works, either.
It's important that any evidence provided actually tests the claim being made. Generally speaking, you can "train" your brain doing any task, and more time spent on a task will tend to make you better at that task. So, if you design a visual task that requires both hemispheres to be involved, and requires some communication between them, you can probably design an experiment to measure that activity and that communication. Does that mean "communication between hemispheres improved?" Not necessarily, it just means you've found a task where both hemispheres are involved. If you train your brain to cross your eyes, will it get easier to cross your eyes? Probably. Will it help you solve math problems? Probably not. If someone says "increasing the "processing power" of your conscious activity" you should be thinking "How do they define 'processing power'? What practical use have they connected this to? What actual benefit has been demonstrated?" The phrase is meaningless without definition.