I have that Galls bag at home. IIRC, it just has a zippered mesh pocket on the underside of the lid; not nearly big enough for a collar. I suppose you could fit it flat on top of the rest of the bag, but you'd be shoving it out of the way every time you opened the bag and didn't need it.
"Opportunity is missed by most people because it comes dressed in overalls and looks like work." -- Thomas Edison