No.
Some NHL goalies who wear the helmet/cage combo:
Dominik Hasek
Dan Cloutier
Martin Prusek
Chris Osgood
I would consider the helmet/cage combo to be a form of mask. While it may not completely conceal the face, it certainly covers as much of it as Robin The Boy Wonder's mask does. And what about Captain America's sidekick, Bucky Barnes? His "mask" was barely more than a line drawing around his eyes.
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Legend, oh legend, the third wheel legend...always in the way.