I've had it done before I knew I had ME/CFS. I would not recommend it. There's not really much that can be done to treat the results.
I saw one and got the testing done after my HBOT doctor said he sends his patients involved with his studies to one. It was an all day of IQ tests and memory tests. I was totally whiped and had a bad "brain-ache," which I use to describe having mental PEM. It's not a headache, but rather feels like what your brain feels after finals exams in HS or college after weeks of long study days and long exams.
It didn't really provide me with any new information that I didn't already know from my SPECT scan and HBOT consult. The neuropsych testing showed that I had exceptionally high IQ and top percentiles in most testing except for areas of the brain that showed poor perfusion on the SPECT scan in the prefrontal cortex and lymbic system. The neuropsych testing also confirmed my exhibited cognitive symptoms: poor memory, poor word finding, poor decision making, very fluency, slow reaction, poor attention. In those areas where I had poor perfusion and had physical symptomse, I still tested "normal" on the neuropsych exam basically 70%ile. But these numbers were significantly lower than my IQ and other test areas of the brain where I scored >95%ile, so it was obvious I had problems there. It was actually a key insight by the neuropsychologist.
There wasn't anything the neuropsychologist could offer in terms of treatment. She basically said do crosswords and sudoku when I presented her information about brain plasticity and neuro-reprogramming. HBOT was the main course of treatment. She said that she could do another round of neuropsych testing after my HBOT treatment, but that it wouldn't be very useful as individuals with my intelligence level are too smart for the exam after doing it once.
I will say however, my HBOT treatment did help me with some of my cognifitive problems. It didn't cure all of them, but improved. I no longer have such extended pauses in my speech, searching for words. My memory is improved but not cured. My "brain-ache" or mental PEM is constant 24/7 anymore. My decision making is better (no longer changing outfits 3 times for the day like I used to).
In short, my neuro-psych testing confirmed my SPECT scans, which basically similar to SPECT scans on other CFS patients. My cognitive symptoms seemed to line up exactly with the neuro-psych testing and SPECT scans. So, no. I would not recommend it. It's helpful if you're at the beginning of the journey, trying to figure what's wrong and show that something's wrong. But many tests done after having proven one has CFS is kind of useless in my opinion, because there's nothing that can be done with the test results a lot of the time. It's adds more documentation and confirmation of symptoms.