In terms of wearing hearing protection, it appears not. I simply cannot find and mention of men blocking their ear canals: there was minimal cognizance and association of loud noises with deafness; this did not appear until studies of miners in the 18^th century made the correlation. Early medicine felt that loud noises were something that was "to be built a tolerance against"... essentially that you had to have repeated exposure to gunfire's noise to gain "immunity" from it's hearing damage. I recall no records of men using foreign objects in their ears in this era; maybe another Redditor will have better luck? As well, the need to hear commands by line officers far outweighed any notion of hearing preservation.
As for sources citing the damage that soldiers sustained from gunfire, this is documented. Records go back as far as the 16^th century when a French Surgeon, Ambroise Paré {1510-1590} documented that "one often sees gunners losing their hearing because of the great agitation of the air inside of the ear." ^1 He had also documented "the great thunderous noise, large bells, and artillery" of warfare. ^1
Soldiers did report hearing loss. I am having trouble finding sources for the 18th century, but documentation exists of General Washington being hard of hearing in his later years; as well, many of the men who fought on both sides of the U.S. War for Independence also reported losing hearing after line battles, and of being deaf or hard of hearing in their old age.
Although 19th century, it is important to note that the decibel levels of firearms and tactics had not significantly changed between Revolutionary era soldiers and U.S. Civil War era. Veteran's compensation in the United States goes back as far as the Civil war, and those data show that as much as 33% of Union Soldiers claimed hearing loss post war. ^2
There does not appear to be a concerted effort by any military forces to protect hearing until the 20^th century advent of the jet engine ^3. Although, I found evidence that WWII Naval gunners, especially turret gunners, had boosted headphone protection... although this was more likely for communication value vs. hearing protection.
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