Um...no.
Geoffrey DeHavilland himself wrote to the air ministry pitching his concept as a light bomber that was fast enough that little or no defensive armament was needed.
He wasn't selling a fighter.
In September 1939 DeHavilland went to the Air Ministry to pitch the light bomber version, however in November 1939 according to Martin Bowman in his book DeHavilland Mosquito:
"In November various long-range and escort fighter developments as well as bomber, fighter and reconnaissance versions were looked at and a conference was called with Wilfred Freeman to consider all the proposals."
He was selling fighters as well at the point.
According to William Green in Famous Bombers of the Second World War
" On its own initiative, however, DeHaviland team designed their aeroplane from the outset with provision for guns or cameras so that it could serve equally well as bomber, fighter or photo-reconnaissance aircraft……"
According to Simon in Mosquito the Original Multi-Role Combat Aircraft
"Chief Designer for DeHavilland, Ronald E. Bishop, already had his eye on basic versatility, for all the while during the design studies he made sure that there was always space under the floor for four 20mm cannon." I wish I could find my copy of the Wooden Wonder by Bishop to hear (read) it straight from the horse's mouth.
On March 1 1940 a contract for 50 Mosquito bombers was placed, however 3 months later on June 10 1940 the contract was amended to 10 PR 1, 30 F II, 10 B IV. And that's how they were completed. Obviously a fighter was in DeHaviland's plans all along. The next order was for 150 Mosquitoes of unspecified type was placed on December 30, 1940 but that was amended in April 1941 to 150 fighters with an additional 50 fighters added. Yet another 50 fighters were added. At this point there were 280 fighters on order with only the original 10 PR Is and 9 B IVs built.
Simon: "At last, in mid-July, a first mention of the bomber variant was made in the order schedule. It was now requested that the last ten PR machines in Contract 69990 be converted to unarmed bombers, together with the last 50 machines in Contract no 555, but was also stated that it was hoped these would have some form of fixed forward armament." Contract 555 was the order for fighters I previously mentioned, however the fixed forward armament sounds like a fighter bomber variant.
I have compiled the production numbers for the primary war time versions
2/3 of production were armed with 4 20mm cannon. The Mosquito was a fighter first and foremost.