Yes, from recordings I'm familiar with Mann played mainly flute.
Frog might jump in with his usual musical expertise but I believe it may be more common for reed players to master more than one instrument that those in other instrument groups. Many tenor sax players also performed on soprano for example (similar fingering?). In the case of Herbie I believe he played regular clarinet as well a bass clarinet while focusing mainly on flute. Certainly that was his focus as his career developed.
Frog might jump in with his usual musical expertise but I believe it may be more common for reed players to master more than one instrument that those in other instrument groups. Many tenor sax players also performed on soprano for example (similar fingering?). In the case of Herbie I believe he played regular clarinet as well a bass clarinet while focusing mainly on flute. Certainly that was his focus as his career developed.