You have the correct idea.
Machinegun installations in single-engined biplanes only evolved slowly between the wars.
Remember that WW1-vintage biplanes barely had enough horsepower to loft one or two rifle-calibre (.30”) machineguns. Naturally these were mounted to the strongest part of the airframe: the center fuselage. Synchronizing them to fire through propellers was challenging.
MG installations started out outside the center fuselage (Sopwith Pup) then into rudimentary fairings (Sopwith Camel), finally inside the fuselage mold lines and firing between cylinders (Gloster Gauntlet). While Gauntlet managed to eliminate profile drag, they still struggled to synchronize bullets with blades. Synchronizers limited the numbers of bullets that could be fired per pass. As airplane closing speeds increased, pilots repeatedly asked for more rounds per second. Note how ground-bound WW2 Browning .303 MGs typically fired 600 rounds per minute while aerial variants fired at twice that rate.
This tradition continued into WW2 with first-generation monoplanes (Me-109, , Moraine-Saulnier 406, Yaks, Curtiss Hawks and even P-51A mounting .30 or .50 calibre MGs in the engine cowling synchronized to fire through the prop blades.
Synchronization became more difficult as open-bolt MGs and auto-cannons were introduced. Open-bolts are better for cooling and preventing hang-fires, but their longer dwell-time increases the risk of shooting a propeller blade. Even a fraction of a second delay in sending a bullet down the barrel can “hole” a prop blade.
Gloster Gauntlet was one of the few inter-war biplanes fitted with MGs in the lower wings. Gloster also experimented with mounting MGs on the top wings and it is rumoured that Gauntlets defending Malta were also retrofitted with guns on the upper wings.
Wing-mounted MGs - on monoplanes - needed to wait until engines consistently produced more than 1,000 hp. and engineers learned how to build stress-skin, cantilever wings.
