I...assume so, judging from the way he's talking here. But given that he's kind of on the outskirts of "the good guys", that kind of undermines the idea of Batman dying being something of a rumour and not a confirmed fact.
(Which doesn't make any sense at all IMO, when you had Superman flying around with a charred Bat-corpse. How was that not caught on camera? Or maybe Gotham just completely isolates itself from outside news sources.)
On the other hand, if he did know, you'd think he'd be flipping out/angsting over why Batman would be willing to shoot Darkseid and not the Joker.