Are you using a Student version of AutoCAD? Because that's the only free version that I'm aware of. AutoCAD is normally around $1500/month, or a little more maybe.
No, AutoCAD does not generate g-code.
Here is the typical workflow, when using AutoCAD.
1) In AutoCAD, you either create a 2D drawing, or a 3D model, and save or export them.
2) You import the 2D drawing or 3D model into a CAM program.
3) In your CAM program, you create toolpaths from your imported drawing or model.
4) While still in your CAM program, you then export g-code from your toolpaths.
5) You open the g-code with Mach3, and run your parts.
Mach3 does come with a very basic CAM program called LazyCAM. I don't recommend using it, though, as it's quirky, buggy, unfinished and unsupported.
There is a method to get g-code from within AutoCAD, which is what I do. I wrote a VBA macro to export g-code for a 2D drawing. You basically draw your toolpaths, and the macro exports the g-code. Here's a link.
http://home.comcast.net/~cncwoodworker/AC2GC.html