If you follow the Wild Mass Guessing theory that the end credits show how Panty and Stocking's mortal selves died, they could be one, despite the happy smiles of the bobble-headed chibi characters. The ending credits show them being attacked by a monster, strapped under a descending circular saw, and attacked by vultures in the desert, before ascending to Heaven, all to the tune of Mitsunori Ikeda's "Fallen Angel", a tear-jerking song in itself.
The Shoot the Shaggy Dog moment at the end of Pulp Addiction counts in typical PSG fashion.
The fact that the creator has left GAINAX to make his own studio, marks as a Tearjerker of itself. Combined with the fact of What GAINAX makesnow, that we will never see GAINAX make something this awesome ever again.