They cancelled the major PvE part they were apparently working on, but they’ve had small PvE game modes that are mostly just wave defense. There’s a Halloween one called Junkenstein’s revenge, this season has one called Trials of Sanctuary, last season had one whose name I can’t remember. None of them are near the scope of the cancelled PvE, though.
Not even one full round (startrek.website)
Activision Explains Huge Call of Duty Modern Warfare 3 File Sizes (www.ign.com)