I don't have a CaravanStore, but have been interested in them since getting a suitable caravan. Personally, I'd be inclined to remove it, depending on how long the van would lay idle, how much of a faff it was and how much space it would take up in storage either inside the van or in a garage.
Slightly off topic, but how far down does the 'bag' hang from the awning rail?
Our caravan has the awning light above the door, really close to the rail and I think it would be damaged by a roll-up awning. As i would want the CaravanStore to function primarily as a rain canopy, i'd want it as far forward as possible.