If you reside in a county that requires emissions testing, you are required to obtain an emissions test when initially titling and registering your vehicle or annually to renew your registration regardless of whether the vehicle is rebuilt or not. A vehicle being rebuilt cannot be driven on the roads until the rebuilt process has been appropriately completed and approved. For the registration on that vehicle to be renewed, it must pass the emissions test.
Reference: Tenn. Code Ann. § 55-4-101(d)(2)