No, and they are not even close to doing so.
There was one SpaceShip Two, named VSS Enterprise. It suffered a crash on its fourth powered test flight, before achieving the license to carry passengers.
Quoting from WP: Virgin Galactic, emphasis mine:
By September of 2014, the three test flights of the SS2 had only reached an altitude of around 71,000 ft, approximately 13 miles; in order to receive a Federal Aviation Administration licence to carry passengers, the craft needs to complete test missions at full speed and 62-mile height.
[...]
At 10.51am PST 31 October 2014, the fourth rocket-powered test flight of one of the company's SpaceShipTwo craft, VSS Enterprise, ended in disaster, as it broke apart in midair...
The second SpaceShip Two, named VSS Unity, is still undergoing test flights.
- Flight 13, on 2018-05-29, tested the changed center of gravity as passenger seats carried for the first time.
- Flight 14, on 2018-07-26, reached the Mesosphere for the first time (52km of altitude).
These are the last two test flights at the time of this writing. No license to carry passengers, and even the test flights haven't crossed the Kármán line into space yet (100km of altitude), or even the USAAF more generous definition of 80km of altitude.
So, no passengers, and no "space".