Does the any part of the stem EVER connect to the fork? In any model?
 

Especially in modern stems, where they come in 2 pieces, does the stem ever connect to the fork?

I'm referring to the part does directly comes out of the headset, does it connect to the fork?

Thank You.

Well they have to connect to the fork or you couldn't steer the bicycle. I think you have a misunderstanding of what the parts involved are. The fork has a steer tube. The stem is a separate part that connects to a steer tube via some clamping mechanism. Here's picture of a fork/stem/handlebar without the bicycle in the way
http://i144.photobucket.com/albums/r...e/IMG_0765.jpg
The stem clamps onto the steer tube so that you can move the fork.

In a threaded fork, the stem is clamped to the steer tube via a wedge mechanism. The wedge is pulled up against the inside of the steer tube.

Stems for threaded are innies, for unthreaded, outies.