Yes, in casual speech. At least in my family - but I grew up in the US with immigrant relatives, so I can't speak for natives speaking modern Moscow Russian... But yes, I've heard it all my life: "Ну, пора," meaning, "Well, it's time." The context would be in the way of "let's go/get going, let's get started, time to leave, those chores aren't going to do themselves..." Or sometimes it would indicate, "Turn on the TV, the show is starting."
Can we drop "идти" and get the same meaning? I asked because a sentence in Duo was "Мне пора на работу" and translated as "It is time for me to go to work"