Unfortunately, No you can't.

You can however Select the Sub-D face and Refine it (Add more divisions) and then use the new divisions to build up a new form, But i don't like doing this much as it really can dense your mesh up really fast, and consequently slow your machine down considerably.

You can (while in polygon mode) add more Geometry, by putting in new edge loops using the "Insert edge loop tool", and the "Split Polygon tool" though you have to be careful not to let your mesh get messy (no 3 sided or more than 4 sided faces, or holes) as Sub-Ds will soon get very, and irreversibly Buggy! But if you play your cards right and perform your operations smartly, you can practically rebuild your Poly mesh while in sub-Ds. Using such tools as the "Append to polygon tool" "poke face", " Wedge face" "Extrude" pretty much all the poly editing tools.

Anyhow, if (after you've converted to Sub-Ds) realize that your Poly mesh doesn't have enough Geometry to complete the task at hand, you can Smooth the poly mesh.
This should give you the ability do define enough surface detail to perform your operation.

Hope this help