A rocket troop of the Royal Horse Artillery (Whinyates's) did participate in the campaigns in Central Europe, culminating in the battle of Leipzig. I believe they were part of Bernadotte's Army of the North (Steding's Swedish Corps, Bulow's Prussian Korps, and Winzingerode's Russians).

Their horses and discipline attracted admiration from allied officers (including Blucher), but not the Congreve rockets with which they were armed.

In any case, there were over 1000 guns in the allied army at Leipzig. A single RHA troop (battery, or company in other armies) would make little difference among such a large number.

Unlike infantry or cavalry officers who either purchased their commissions (or were promoted from the ranks surprisingly often during the Napoleonic Wars), and who subsequently learned their trade "on the job", Royal Artillery (and RHA and Royal Engineer) officers had to attend the Military Academy at Woolwich. They were therefore career and professional soldiers, unlike Hobbitmum's gentleman adventurer.

The system of purchase of commissions didn't do as much harm during the Napoleonic Wars as it did during the subsequent peace, because so many units were engaged in hard service that senior officers died quickly or were only to glad to sell their commissions at their face value. (During the peace of 1815 - 1854, wealthy officers like Lord Cardigan could purchase their commissions after an unseemly auction, which drove the price of promotion far beyond the means of officers from less exalted backgrounds.)

A toast among subalterns in the British Army which was (is ?) drunk before leaving Britain for active service in wartime, goes "A bloody campaign and a sickly season !" There is nothing like cannon fire, yellow fever and dysentery for clearing the dead wood among senior officers, and allowing quick promotion to deserving and lucky junior officers.