I vote for yes--we always take it with when we go, for several reasons. It is fun to record your child(ren)'s interactions with the characters, as well as other special things like parades, shows, etc. Also, it is fun to show family members when you get back and it gives them a better visual of WDW than random photos.
As for storing it, we (I) always bring it with on the rides. I put it in between my feet and sometimes put the strap around my leg if it is a faster ride. Our bag for it is bigger as well, but we keep other stuff in it--our digital camera, some wet wipes, my wallet, etc. so it is more like a purse/diaper bag. We don't carry any other bags.
Hope this helps!