Do I need premium process?

I am working for University under my OPT. My OPT will expire on 12/10/04. The university I am working for sponsored my H1b application which will start on 12/01/04. The International program of University filled my application late July as regualr H1b application to Texas service center. The application was received by USCIS on 08/05/04.

Can I get approval notice before my OPT expires? Do I need to file premium process? Based on the online processing date, I-129 change of status in US is May 27, 04. I am afraid that they will not have chance to process my application before my OPT expires.

Thank you for any suggestions !!!