You should be able to renew with i-797 approval notice, but it would most likely will not create a hit and be sent to secondary review and it would take time for you to receive your license. It's best to wait until you get your work permit.
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Application Sent - 9/19 (Phoenix Lockbox)
Routed to: California
Delivered - 9/21
G1145 Notice - 9/26
Date of I-797 C Notice of Action - 9/28
Date of Biometrics Appointment - 10/18
Walk in 10/1
Approved - 10/10/2012 at 3:45 pm
EAD Received - 10/15/2012