It depends on how the data was stored. When the game was live, Fog of War had two distinct states: when you first navigate a zone, it's blocky and very jagged when you're in the same session. Once you zone out and return, the server had a "softer" and more precise image of the areas you've already navigated.
This seems to be two different methods of recalling the zone: one done by the client as a 'preview' of the lifted fog in a zone. The second being the server returning precise data on each coordinate you've visited, with more 'preview' fog lifted as you navigate more of the zone.
So if we're talking about a "bitmap" (not necessarily a picture, but a 2D representation of every area you've visited) of the zone based on the coordinates that the player has discovered (not all three, of course, just X and Y) then a copy of that bitmap has to exist for all zones that the player has visited, and especially badge hunting, every Fog of War map in the database would have a list of all the X and Y coords. visited by the player. This info would be kept in the database per character. That's 48 characters with individual bitmaps of the zones they've visited. It's not a negligible amount of information: if you consider someone has the full complement of 48 characters on the account given, multiplied by the number of maps present on Paragon Chat (if you don't use quickchat, about 60 zones... if you do, hundreds.) then enabling Fog of War on all of the maps in the extreme case might be a lot of work for a little payoff.
As the badges are in the 60 zones and not in the encounter and instance maps... If we're talking the city zones, PVP areas, tutorials, and co-op areas ... that might be the most prudent to ask.
The other part to consider, as well: edge cases. Two areas in particular -- Pocket D in Paragon Chat has another meeting place that's not a part of the original client. And the Abandoned Sewer Zone has a kitbashed map to allow users to collect the Head of the Hydra badge, which is 50% city zone, 50% instance map. Those would be difficult in either case.
Full disclosure: I have to disclaim here that I'm not a programmer, and I'm not a part of Paragon Chat development, but hopefully that's a clearer picture of what it looks like. Ultimately, CodeWalker would make the determination.