Does the integrated Intel Iris Pro GPU support an external display? I have a MacBook Pro (Retina, 15-inch, Late 2013.) This model has an built-in Intel Iris Pro GPU and a dedicated GeForce GPU. 

Without an external display, the integrated GPU is active and the dedicated GPU is idle.

After I connect an external display, the built-in GPU is idle and the dedicated GPU is active. Power consumption nearly doubles, the system get hotter and the fans turn on.

I expected the dedicated GeForce GPU to only take over when the intensive graphic programs are running, not when running Safari on two displays. 

Does the integrated GPU support two displays?

If yes, then how can I get the integrated GPU to support two displays?
The external graphics port(s) are literally wired to the discrete graphics chip.  The only card that has access to the TB port is the AMD dedicated card. That's the same reason why you need the AMD card enabled to do anything with the TB port. 
 This is why connecting an external monitor will always (regardless of method of deactivating the discrete graphics) enable the discrete graphics.