Rather unlikely. To start with, you can hardly mount even a single falconet on a horse
and ride it (horse, not falconet) and on a camel they were quite often mounting two falconets/zamburaks (see mounting below).
View attachment 561208
Then, how would you fire it while riding ?
View attachment 561209
In a kneeling position it would be much lower than when on camel’s back and would not be very convenient to use
View attachment 561210
Zamburak caliber was 40-65mm with the cannonball weight between 300 and 800 gram. So you’d need to place, besides a rider and falconet itself (*), 40 cannonballs (each weighting between 300 and 800 grams). Quite an extra burden for an average horse.
And advantage for the ...er... “Western” (😜) usage at the time of Napoleon would be what? By the late XVIII the falconets were still used in the “peripheral” wars (seemingly were in use during ARW) but in Europe even 3 pounders had been steadily squeezed out by the heavier calibers and zamburaks were one-/two-pownders.
The Iranian Quajar army had the regiments of the zamburaks and it was beaten by the Russians. Zamburaks were used against the invading
British in the
Anglo-Afghan Wars and in the
Anglo-Sikh wars and who ended up winning? Actually, the Brits did some useful adoptation of the idea: after 1850,
Gatling guns were mounted on camels.
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(*) Barrel of the European falconet with a caliber 50mm (2 inches) had been weighting between 80 and 200 kg. Add a lighter version to a total weight and your horse would have to carry, besides a rider, an extra 100kg. Even if we assume that the “Eastern” version was shorter and lighter than “Western” one, this would come at a loss of the range and firepower.