Comedians only really ad-lib to the extent you're suggesting if they're being heckled or if the setting calls for it, like Whose Line?. But jokes intended for a set tend to be thought about, written, and re-written until it feels right, at which point it's test run on an audience wherein they may fine tune it later if they didn't get the response they wanted. But the main point is, a comedian worth their salt won't make the mistake of fundamentally writing a Holocaust joke wherein the ultimate punchline is the Jewish people for having the gall to be victims to it. It's such an easy trap to fall into that most just, well, don't, which shows just how thoughtless PDP was. He, like most other people, think that just by kidding around you get a free pass to say anything you want to.
A joke misfiring doesn't make a Nazi. However, being an asshole to strangers while also slapping on crude Nazi jokes does at least make one not all that sympathetic to Jewish people either.
And just as I said before, satire is meant to expose a problem with people or society by highlighting their flaws while also making a call to action. There's nothing flawed with not speaking English, nor is he providing a call to action for anything even if not speaking English was a problem. Seriously, if just pointing out how every human being on Earth is subject to persuasion is satire then literally every practical joke would fall under satire.