Can you time-shift live programming?
In a limited sense, yes. Live programming on PlayStation consoles can be paused for up to 30 minutes. On certain other devices, like Fire TV, the video immediately resumes playing after a brief interval. Additionally, you can't manually fast through the time-shifted video on some networks, like ESPN and Comedy Central, without going back to the live feed.
In other words, you can take brief bathroom or snack breaks with PlayStation Vue's time-shifting features, but you can't always pause a show and then skip through all the ads.