I am not sure that a lack of functioning due to cognitive abilities necessarily renders a person mentally ill. Agreed cognitive disability occurs within mental illness most especially schizophrenia but not all people with cognitive inabilities exhibit signs indicative of a mental illness.
I agree that a reduction in occupational/social functioning is something that can and does occur in people who have symptoms that are seen as pointing to mental illness.
Indeed cognitive disability whether it be in terms of an overall ie generalised reduction in cognitive ability or specific areas of reduced intellectual functioning is reckoned to play a part in the ability to function successfully both socially and occupationally.