They did, but some of the vehicles it was applied to weren't very...super.
SS to me means GM marketing couldn't think of a better name after the bean counters and bankruptcy killed off the planned move of the Impala to Zeta which is what this car really was supposed to be. Then they obviously couldn't call it an Impala SS once they kept that car FWD.
The first use of the term Super Sport by Chevrolet was in 1956 on a special Corvette show car. It was used again in 1957 on a special order Corvettes for race use only. Then in 1961 Chevrolet finally brought out their first Super Sport package with trim and other mods to a stock vehicle. The Super Sport moniker has continued ever since in many various forms usually associated with higher performance models. However, I don't quite understand how pickup trucks ever qualified as Super Sport vehicles, but anything goes in order to sell vehicles I guess.