do you guys think gordon wears a helmet
His hl1 model dosen't have a helmet, His deathmatch model dosen't have a helmet, there's no official half-life artwork where gordon uses a helmet
No, but in Half-Life: Extended, yes, but no.
he dosen't wear one
This is the most debatable thing that has the most straight answer.
In the half life 2 banner page on the steam library, we clearly see Gordon with no helmet and only his glasses.
If you search for Gordon Freeman and open images in Google, there is no image of him wearing a helmet. And most of the images are from valve
Tldr, no, he didn't wear a helmet.