Oh boy. OK, a passport can prove he entered the country legally, but not that he remained here legally after his date to leave passed.
I can not check is status, as that is private, highly confidential information between he and the Immigration agency.
I am confused though, if he deported himself, does that mean he is no longer in the USA? Or did he get back in?
But moving on. generally one can't collect SS while not legally present. He can potentially collect if he leaves, but, what he will likely want to do if he wishes to stay here is consult with an Immigration lawyer to determine how best to become legally present.
The statement about not trying for a visa because he has legally deported himself is not really clear to me - since he is clearly not deported. But, that said, he really needs to address his non-legal status and get it resolved if collecting his SS benefits is important to him. It may mean leaving for a while, and coming back in legally, having perhaps applied for a visa and then green card.
So, in answer to your question, no, generally non-legal status (no green card, no visa, and not a citizen) means no SS will be paid, unless and until he fixes that OR, decides to collect while present elsewhere. SO that he is not "non legally present" here.