No, they are NOT.
Air Atlanta Icelandic’s main focus, revenue and fleet is the Passenger operation, with both B747-400 and A340.
They're ostensibly a charter airline/leasing outfit, mostly focusing on 747Fs and Haji 747s. They don't have, and never did have, any A340s. Not sure what you're on about here...
My dear , as a Captain for AAI, I do think I know which aircraft are in our fleet...
TF-EAB, currently undergoing maintenance but back Operating next week.
Also, most flights with our passenger aircraft are nowadays regular Scheduled flights for SV, combined with Umrah and during the season, indeed exclusively Hajj.
Sorry, I forgot about -EAB! Just went by the fleetpage on the AAI website.
But regardless, as mentioned above, FI had 6 times more revenue than CC in 2017, plus their operations (and WOW's for that matter) don't have too much effects on the Icelandic economy as they don't fly pax/freight to or from Iceland on a regular basis.
As an aside, perhaps the favorite flights in my log are AAI 742s/743s to the Canary Islands, Spain and Portugal in the early 2000s, sitting in the nose or on the UD.