That's a terrible idea. If you crash, that helmet will be wearing your arm for protection. As GreyGhost mentioned, no solid objects on you or your backpack that can cause serious damage in a crash. I've used a bungee net with the helmet on the passenger seat, the odd time I had to carry it.
I think he is referrring to a top box. I have used the hook before, for me it made no difference to the feel/handling/body position required so highway/twisty wouldn't matter. It did bang around a bit so I wouldn't do it for a long time or with a really good lid.
You can always carry a cruiser style (DOT) brain bucket half helmet in a tank bag. Have the class to let your passenger wear your full face (assuming it fits and is not funky inside) and you the crap helmet, make sure to have glasses. Depending on the tank bag you may even get a proper helmet in it.