I think it's okay.

Some weeks I need to travel with a hard hat to do site visits. I always strap it to my top backpack handle.

I am always able to get on the plane with my backpack my roller board and my hard hat attached to my backpack.

It all fits under the seat in front of me if needed. Plus, I figure if I'm ever challenged on it I'll just wear the hard hat onto the plane as my super cool fashion accessory.

Only thing I find is people ask you what kind of work you do way more while you are traveling with a hard hat than not.