Yes, it is possible.
This is the copy of a press release earlier this year:
Three Virgin Atlantic pilots have already been handpicked on the basis of their experience and skills. Steve Johnson, currently a training Captain with Virgin Atlantic and an ex-Red Arrows pilot, will become the chief astronaut pilot for Virgin Galactic, having overall responsibility for the pilot astronaut workforce.
The pilots will receive nine months of aerobatic, fast jet and executive aircraft for zero gravity flights training. They will then spend the next nine months flying the mothership and participating in Mission Control work - the last nine months will be spent flying Virgin Galactic Spaceships into space. Once they have completed their 27 month secondment they will return to Virgin Atlantic as qualified pilot astronauts.
From 2008 Virgin Galactic expects to have around 30 astronaut pilots recruited from all of the Virgin airlines round the world. 50% of the astronaut pilots will be recruited from NASA and Virgin America with the remaining 50% being recruited from other Virgin airlines including Virgin Atlantic from which three pilots will be seconded. Virgin Galactic also plans to recruit some of its pilots from Virgin Nigeria, Virgin Blue and Virgin Express. In December Virgin Atlantic launched the first frequent flyer programme reward where Flying Club members could earn miles to get themselves to space.
Virgin Galactic is a company established by Richard Branson's Virgin Group to undertake the challenge of developing space tourism for everybody. It will own and operate privately built spaceships, modeled on the history-making SpaceShipOne craft. These spaceships will allow affordable sub-orbital space tourism for the first time in our history. Every customer of Virgin Galactic will be helping the development of a new generation of space craft.
Scroggs