I think seeing the Joker weep would be enough to leave her speechless all the same.
There is also another instance of the Joker crying, btw. A Pre-Crisis issue of Brave and the Bold where he teamed up with Batman to find the Penguin's murderer; he actually shed a quiet tear when he saw Oswald's (fake) corpse, and Batman was actually surprised that Joker's mourning appeared sincere -something quite beliuevable since Joker didn't make a show of it. of course, when he found out he'd been had, he later tried to kill Oswald himself.
This was the old Joker and not the uber-Joker born from The Killing Joke and arkham Asylum, but I still think that would make sense for the current Joker; he probably saw the Penguin as part of the weird, wild world of Gotham, and was sad as seeing such a singular character vanish from that world -it's pretty obvious that Oswald ranks high in the weird Gotham underworld, and I can see Joker having a high appreciation for all things weird (I still haven't figured out the connection between penguins and umbrellas, myself).