Given you can't run most games on current-gen consoles offline I'm not sure that's the point you think it is.
Well, you've asked if it's possible, not if it's practical and convenient under any circumstances.
I can't edit my comment. Console vendors don't envision consoles as general computing devices, which kind of tends to end any sparky comments one might make on the topic.
Apple also doesn’t envision that you can run arbitrary root code on an iPhone either