I'm sure there are car designers and engineers who play GT, so yes, if they all got together they would probably be able to design something. But the World isn't the same place as it was 50, 60 years ago, and getting it built is another matter entirely. There are many more regulations (e.g. safety & emissions), and you would still need a huge amount in capital investment to get something to production.
And the World is littered with bankrupt small car manufacturers (Fisker being the most recent example), as well as a volume manufacturers too (e.g. Saab). There are a few successful independents (e.g. Pagani, Caterham, Atom), but these tend to be building for a specialist market. There are none, as far as I can remember, building anything for the mass market. One of the best engineers in motoring (Gordon Murray) has even struggled to get someone to build his city car project.
So could a group of properly qualified people build a car? Yes, of course it's possible. But what does GT have to do with this other than the coincidence of qualified people playing the game?