One does not "register" as a handicapped person with ADA. I am sure that your son's employer is quite aware of his limitations, regardless of whether you talk to them or not. The Americans With Disabilities Act does not get one a job, is not an entitly, rather it is a federal statue that indicates a person who has a limitation or disability may not be disqualified for an opportunity for which he is otherwise qualified due to his disability.
If he is counseled by his employer regarding his performance, this is in no way a violation of his EEOC or ADA rights. If he were to be terminated by his employer for performance issues, with a series of progressive disciplinary actions in his file regarding his job performance, there would be no potential lawsuit because of this. They have not violated any rights of his,he has just failed to meet their performance standards. I am sure they are already making considerable accomodation to allow him to perform the job.
He could file for employment insurance because he is actually terminated for a non-misconduct reason, and all he would need to say is that he was doing his best on the job and that he was unable to meet their standards of performance. Then he would be able to draw benefits for a limited time and seek other appropriate employment.
However, even if a person has a disability, this does not render them "termination proof" or say that the employer has to put up with genuine misbehavior and/or poor performance just because this person has intellectual or physical limitations. It is not in the best interests of the employer to allow someone to continue working who cannot do the job adequately, and it is NOT required by any law that he do so.