a brief excursion into a very low orbit
Not even that. The mothership launch technology has not yet overcome the technology hurdle to achieve anything better than a brief parabolic excursion beyond the atmosphere. That is why the experimental craft of sixty years ago did not progress further and the space programme reverted to vertical launch rockets. Early ideas that the Space Shuttle might work this way were also quickly abandoned.
For a real technology progression using this launch method a
true hybrid engine would be needed - a combination jet and rocket that can transfer gradually from air-breathing to purely reactive as the air density decreases. And that is a development programme which is probably beyond even Mr Branson's deep pockets.