yes, the certainly did, however a turbocharger's turbine is spun using exhaust gasses and a supercharger uses a direct drive off the crankshaft, which reduces "turbo lag." i am not sure if the allison 1710-89 powerplants had both, at least in the 38's, but it is possible and not unheard of in other applications.
A "Supercharger" is any device that brings the manifold pressure above what would be available in the ambient atmosphere.. It can be exhaust or otherwise driven. The 20-645-E7 EMD has an interesting setup where the turbo shaft has a sprag clutch to the engine so at low rpm it is mecanically driven and when the exhaust flow goes high enough the turbine spins it out of the sprag clutch.
The Continental engine nomenclature even takes this into consideration labeling the engines with a "TS" for "Turbo Supercharged"