Yes, however; from a gameplay perspective it wouldn't be smart. Vision is arguable one of the most important parts of a game, if you can't see, it would be hard to play. I am sure some parts of the game would require you to notice a lever or button, spot a trap and such. You couldn't do that with limited eyesight.
Though I do agree, I have noticed that many helmets don't have actual bottoms. The usually cut off at the nose, looking down to see a trap wouldn't be hard. On the other hand, It would be very hard to see other enemies while focused on one opponent, so in truth, your post is very correct.