Can a request be made to an accident repair shop to declare a car totaled?

Ultimately, the decision to declare a vehicle a total loss belongs to the insurance company. If the insurance company is unable to have one of their own adjusters look at the vehicle, they will usually hire an independent. The repair shop can write an estimate and take pictures, but the insurance company will decide (based on state law and their own policies) whether or not the vehicle is a total loss.