Possibly do some good, but look at cost versus benefit

The protection in the field is almost entirely that of camouflage dictated by the immediate surrounding appearance of woods and shrub brush, not uniform or command.

It’s a hat to hold over your heart and sing the national anthem. Perhaps some importance or attention to detail is warranted, but not to overshadow the country or the person wearing it, other than the cordial dress.

A Pentagon test group is eyeing these ballistic ball and patrol caps for troops
The protective hats could shield service members facing threats in places where patrol caps, not helmets, are the norm.

If the fabric is Kevlar or some bullet-stopping fabric, it may, for the small physical coverage it affords, chance to prevent a brain injury from small arms fire or a stray piece of fine small shrapnel.

Or even if the skull is fractured, the fabric may still prevent the projectile from penetrating brain tissue.

The camouflage color is good of course.

Other than that, it’s a hat to doff for the ladies or throw where you feel at home or toss in the ring for a fight.

And keep track of it and don’t lose it.