There is very good evidence that aerobic exercise improves cognition in other groups, with particularly good evidence in ageing people, and rodents(!), suggesting that it may be beneficial for brain health generally. There isn't strong evidence for it doing so following concussion, but then there isn't much evidence for any interventions following concussion because most researchers are only interested in finding out whether our symptoms are organic or psychological, rather than finding out how to get rid of them.

Interestingly, if our symptoms were to be found to be entirely psychological, there would likely be an even firmer basis for aerobic exercise which has been found to be at least as beneficial for people with depression as anti-depressants.

My advice (and my interpretation of exercise guidelines) is not that you shouldn't exercise unless you are symptom free, but that you shouldn't exercise if doing so makes your symptoms worse. So when I was recovering I would exercise even though I had permanent slight brain fog and headaches that never went away - as long as these didn't get worse, then I wasn't doing myself any harm by exercising. This seemed to me to be very beneficial, definitely for my mood, and possibly playing a part in the reduction of my symptoms (though I can't prove a causal relationship).