I just put my lid in my top box, but i suppose if your not into having a top box and dont wanna have to carrying you lid about with you it would be a good idea.
I would be afraid of it ripping the seat cover as there doesnt seem to be much room in there. and as GULO said over here in the UK we have alot of little scum bags
who would just knife the strap or the rings off and sell the helmet to some unknowing person.
ah the world we live in today