Ellie, You’ll need follow a few steps, to get the labels to CAD annotation.
1. You’ll need to Create a File Geodatabase and import the shapefile polygons.
2. You need to label the polygons exactly as you described in your post.
3. If you don’t want to see the polygons you’ll need to symbolize them so they are transparent otherwise symbolize them appropriately.
4. You’ll need to set a reference scale<http://desktop.arcgis.com/en/arcmap/latest/map/working-with-arcmap/working-with-data-frame-reference-scales.htm> on your labels so they display at a fixed height and width at the referenced scale on the map. So if you want your text to appear at 12 point font at 1200” scale then you’ll set your font to 12points and your reference scale to 1200” or 100 feet. Then when the map or printed page map scale 100 feet matches the map scale the text will appear as 12 point font. If you zoom out to 2400” or 200 feet then the text size will appear as 6 point font.
5. Convert Labels to Annotation<http://desktop.arcgis.com/en/arcmap/latest/map/working-with-text/converting-labels-to-annotation.htm>
6. Convert Geodatabase to CAD<http://support.esri.com/technical-article/000008383>
Eric J. Rodenberg | Solution Engineer Transportation Practice
Esri | 7775 Walton Pkwy, Suite 270 | New Albany, Ohio 43054-8202 | USA
T 614-933-8698, ext. 5503 | erodenberg@esri.com | esri.com