How to complete 3D Export PCB in Altium
No there isn't a way to export that.
You only can export the 3D models included in your PCB.
There are some tricks for solve this issue but they are really hard and IMHO they don't solve the problem. You can find them in the links below
Here are some topics from Altium Design Forum (you must be registered to see them):
http://forum.live.altium.com/posts/193722
http://forum.live.altium.com/posts/193565
http://forum.live.altium.com/posts/192662
Update:
The format Parasolid allows to export the copper features and Altium export the PCB 3D model in that format