Sure. Though you will have to make sure your artboard size matches the comp size in AE. You may also need to copy&paste something from AI to the clipboard first before being able to do the same from AE... Some weird initialization issue occasionally.
First, your shape layer must be a bezier path or a RotoBezier path. If you used the polygon or ellipse tools to create the shape layer then you must convert the shapes to a path. Second, if the shape path is animated then you must select a single keyframe and copy that. Third, inside Illustrator the easiest way to get this to work is to select the pen tool, create a single point, then paste. If you have an animated path and you select the entire path so that all keyframes are highlighted, then you will get this:
Adobe After Effects 8.0 Keyframe Data
Units Per Second 30
Source Width 1
Source Height 1
Source Pixel Aspect Ratio 1
Comp Pixel Aspect Ratio 1
End of Keyframe Data
So to make this work every time make sure that your shape layer path is a Path and not a shape, set at least one keyframe, copy that keyframe, start a path in AI with the pen tool and paste.