With a stock turbo motor, it probably would be slower. Some engine turbo-engine combos are suited for a manual. Ours are not. Here's some numbers to explain why:
With a stock motor, the power band is 2300 rpm (to spool the turbo) to 5100 rpm (when the heads and cam give up. Not quite as fun as cars that rev to 7K. Slipping the clutch to 2K wouldn't be much fun either. With the auto, you power brake to 2400, shift at 5100 and let the torque do the work.
Put on a larger turbo on and the power band gets narrower. Now it takes 2700 RPM to spool the turbo, but the motor still gives up around 5200 rpm.
So you have to slip the clutch to 2700 rpm (otherwhise you are driving a NA 231 cid V-6), but when you get there you instantly have 500+lb ft of torque. What kind of clutch could take this more than a few times? Or transmission? or tires?
You have to put a cam in and port the heads, change the gearing to make it more suitable and still you aren't as quick as the auto.
With a stage II motor and a race car, a manual might be quicker. The auto has too many advantages for a street car to be quicker, though.