Did any WWII aircraft only use a turbocharger but not a supercharger?
As is suggested in the original question, the answer appears to be "no".  This website gives some hints as to why a gear-driven supercharger would normally be used in addition to a turbosupercharger: http://www.rwebs.net/avhistory/opsman/geturbo/geturbo.htm

(Though the link may raise more questions than it answers: it doesn't make it obvious why a turbosupercharger usually injects air upstream of the carburetor, or why a gear-driven supercharger usually injects air downstream of the carburetor, or why only the latter prevents issues with valve cooling.)