There is actually plenty of research on neurofeedback games, and you will find a lot if you just google it. Frankly, I used to be very skeptic about it by myself, until I had a huge problem with my own brain and tried the technology occasionally.
Being one of ADHD brains, I have found my own way to do the work well - I always needed to be under pressure; the only problem I have is that sometimes my brain just crushes down. I worked fast, I paid attention to things very well when there were lots for them and limitations in time and sources. Naturally, I have realised that no matter what I do - work or hobbies - I always make my life so full of tasks and events that I have no time to sleep. It was exciting and fine until I had realised that from time to time, because I never rest and relax, my brain just collapses once in a few years, when I have a few months when I can't do anything, I just sleep and eat days on a row, having blank mind no matter how I try making it work again. Interestingly, I do exercise and eat healthy food, so nutrition and physics is not an issue.
The thing with brain and especially with ADHD brain for many of us is that you have to realise how much work you can do and to realise what helps you to cope with emotions. Neurofeedback in this case is brilliant, because it shows it to you. I was really skeptic about it's success as I could never imagine how on earth a video game is able to help you achieve something in your life (I haven't had a TV set for 9 years already as I see no point of having them, they usually turn you into a couch potato); but I was exhausted to do my usual staff and i had to do something as I was yet restless and anxious, so I tried around 15 apps because I had them (bought after trying at the event in London "for fun and maybe in case I would ever try to train myself"), and I saw they work. It's not really giving you additional pressure in life if to be honest. What it does help to do, is to realise how to control yourself, and how to SPOT the moments when you go under pressure, and cope with them.
Of course, I am a grown up and I can control my own training and fun. In case of kids, it's definitely the responsibility of parents, as all the child's daily schedule. There are absolutely amazing games developed for kids, they let you train your child, give you daily reports and suggestions, you can change the complexity of the game. I understand that sitting in a classroom with a boring teacher is quite a typical environment, but what happens when the schedules change, when the teachers' number grows, when kids start doing various more complex subjects, have to do assignments, add after-class studies. The thing is, we constantly add pressure into our lives since childhood. Stress is a part of life, and we have to learn how to cope with it. If you can find an entertaining way to help your child to prepare for it, I see no reason why you shouldn't. As with everything else in life while they are young, it is you who has a great control over what they watch and play, whether the pressure is according to their age and capabilities. Maybe try it on yourself, and if you don't think you should use it, don't.