The drunk guy is actually Shalash, and he got rid of his statue using his Heraldic powers because he thought it would be a good practical joke. He's not actually speaking in gibberish, just a language unknown to Szeth.
I had something like this idea on one of the other fan sites, and the main objection I got was that Shalash is almost certainly female, because of the similarity to Shallan's name, and because 5/7 remaining Heralds are female. The drunk was standing between Szeth and a row of Herald statues when he asked, "Have you seen me?" though, which I think is very suspicious. So even if he isn't Shalash, maybe this guy is a Herald who tried to hide as a beggar and forget his past, then got too drunk and started blabbing it to Szeth.