I think its irrelevant whether it shows up in the inventory or not, thats just the way Arma works. What matters is how many you can carry. If it didn't show up, you may well have one less slot to account for that.
The OP's point about rate of fire is totally valid. It should fire the second round as fast as you can click the mouse a second time. As it is now, there is an artificial delay between your first and second shots. It has two triggers.
Maybe even an alternate fire mode that fires both at once would be nice.
The reason for the 2 rounds per inventory slot on the double barrel is Arma 2's design. When you reload a weapon, it has to consume a single inventory item.