Do you really need to convert it back to a non-text shape? If you use the direct select tool instead of the selection tool you can click on the path edge and edit the path, stroke and fill it, etc. But if you really want to, John's reply above hints at a workaround. Delete any text in the shape. Then select the path as I suggest with the direct select tool and give it a fill or stroke. Copy it and paste it into indesign. Select the InDesign shape and paste it back into Illustrator, select it again and go to Object>Clipping Mask>Release, Go to View>Outlines so you can see the rectangular mask , select that rectangle and delete, go back to View>Preview. Phew. Maybe someone has an easier way that lets you stay in Illustrator, but this works.
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