Yes, you can... with the pathfinder tool! Works the same way but keep in mind Mr Pathfinder doesn't like strokes!
You need to make sure the outline (stroke) of your circle is "expanded" first, e.g. not a stroke anymore but a shape.
To do this, select your circle with the outline and go in the menu Object > Expand.
Then you can use the pathfinder tool (divide works well here) and then remove that outline.
To remove the parts you don't need quickly, you can click on that outline slice and then go in the menu Select > Same > Fill & Stroke, and then press delete.
You'll end up with what I think you're explaining in your question... a circle without the outline and within a square.
In my example the outline is thick. You can divide a single path with no thickness or you can expand any stroke and then divide it if you want it to be thicker and have a "visible" transparent outline on your circle.