I don't believe either 2 or 3 had a demo so I doubt 4 will, but they were timed trials through PS+ so maybe SR 4 will be too once it comes out.
Feel free to add me as a friend. Just put "playstation forums" in the friend request.
The "Enter the Dominatrix" DLC hits on October 22. Enter the Dominatrix is the first installment of the Saints Row 4 Season Pass, but it will also be available as a standalone purchase for $7.
The DLC includes an alternate Zin invasion storyline with the Saints trapped in a virtual world run by the AI program known as the Dominatrix – from there it's a battle to survive against sex workers and gimps. Enter the Dominatrix includes new weapons, enemies, allies and missions, and features behind-the-scenes commentary.
Developer Volition will livestream the DLC on October 23 from 1PM - 4PM CT on Twitch.
Enter the Dominatrix was originally planned as an expansion to Saints Row: The Third, and was expected to hit 45 days after Saints Row 4 launched.