May a contractor bid while in the process of obtaining a contractor license, or wait to see if they are awarded the bid, and then apply for a license?

No. Most bids require licensing information on the outside of the bid envelope or the bid will be rejected. Bidding without a license is a class A misdemeanor, and the violator is subject to fines and prohibition from participating in the project (removed). In addition, the contractor license may be held for up to six (6) months from the date the board learns of the violation, or denied.  The only exception would be Federal projects or the Tennessee Department of Transportation for their highway projects.