I don't know if they do. Powerglides are pretty popular. Some of them have air-shifters which don't use a clutch. It depends on what kind of drag car it is.
I don’t think there are many “Turbos” on the drag racing circuit.
Oh sure there are. Happens all the time. Usually twin turbos.
I’d venture to say 70% plus of drag cars are NOT shifted manually.
Lots of HD Powerglides as you pointed out, and the pro classes have air shifted specialty transmissions.