I have a lamp dimmer that I'm hoping that I can use for a project. Before I
go and start a fire or suffer a meltdown I thought it best to ask for
feedback...

At one end of the dimmer there is a polarized plug that you plug into the
wall. The other side of this plug provides a polorized outlet into which you
plug your lamp.

The other end of the dimmer cable is a slider with and LED. Sliding this
control lowers and raises the brightness of the lamp.

What I wish to do is instead of plugging a lamp into the dimmer outlet, I
want to splice into the dimmer cable. I'm assuming that the dimmer outlet is
electrically the same as the wire travelling to the dimmer.

Am I out to lunch on this, or do I have my head on straight?