I wonder what the point there is to an assessment in this situation. Neither the organisation nor the family nor the school (where I assume his behavioural diifficulties come into play) appear to be able to understand giftedness as a concept, let alone be able to do anything about it.
Could you suggest a sort of response to intervention plan? As in, have you tried to give this little boy books? Specifically books for school age children? Tried to let him read to others, write up plans for the day etc. It would be good for both the mom and the little boy to know that they are not alone, but it appears they would be no nearer an actual solution to the problem. Are you in a position to suggest one?