Yup, there were Italian fighters and bombers in the Battle of Britain's latter stages, their lack and the lack of British bombers was one of my main criticisms of BoB2, along with no air/sea rescue elements.
Incidentally, the Italians fared pretty badly.
As a matter of fact, one of my heroes shot down an Italian aircraft in the Battle of Britain (Colin Pinckney). He was one of very few WW2 Allied pilots to shoot down an aircraft from all three Axis powers and I actually have some parts of the Spitfire which he bailed out of during the Battle of Britain (they are severely dented as you can imagine, but there is still paint on one of the panels), an incident which is documented in Richard Hillary's famous book 'The Last Enemy'. I made a slightly dramatised version of that event in this film by the way, R6753 being the Spitfire in question:
You can read about some of Pinckney's exploits here;
http://www.warbirdforum.com/colin.htm
Chock