1. As Abo_Bob said, if you are sensible and drive sedately for the last k or so, then you don't require a TT. (The Shell Sierras would only do a "slow" lap of Sandown after practice, then simply pull into the pit garage and switch off the engine, and they had been pushing 3 bar boost through the engine)
2. The engine will warm up quicker if you drive the car. If you are sensible, and don't pull boost during that period, then no damage is likely to occur. Japs generally don't take care of their engines, so it's likely some old engine oil is baked in the turbo bearings.