Is it possible to have one component displayed with a particular style and another component in the same scene displayed with a different style?
No. (You can combine them in a picture with an image editing program.)
You could try creating two (or more) scenes with the same camera view but two different styles, with different parts hidden, and overlay them in the LayOut application.
I don’t use Layout much so I’m not very knowledgeable about it.
I saw something in the Trimble online documentation about using the “Style tool” and applying it to different entities using different styles. But I don’t see any “style tool” in SketchUp (I’m using 8 Pro) and referenced the scrapbook. So I assumed it must be in Layout. Here is the link:
In the top menu bar click on “window”. Styles is the fifth button down.
I know where the styles window is in SketchUp. The link I referenced refers to a dropper icon that can select a style and a style “tool”.
The styles window in SketchUp does not have a dropper or tool and I don’t see any way to apply a different style to different entities as is described in the link.
The page you referenced describes the style tool in Layout. SketchUp does not have that tool.