Yes, if a person collects SSI or Social Security Disability, that is generally also considered "disabled" for tax purposes.

If (a) your client's AGI is higher than Mom's AGI, (b) the Mom chooses not to claim the disabled brother, and (c) the brother lives with your client, yes, your client should be able to claim the brother as a dependent as all related tax benefits, including the Earned Income Credit (assuming all other requirements are met).