Funny enough, the Lieber Code adopted by the Union during the Civil War, dealing with the rules of warfare, DOES actually prohibit the use of poison, so this idea would have been illegal even at the time.
What was the cost of chlorine at this point? Were they doing chloralkali at any reasonable scale? If so, this would plausibly have changed the entire evolution of warfare in the late 19th century.
Shoot, I probably should have just searched it myself. I guess I was trying to start a conversation.
Depending on how successful chemical warfare hypothetically would have been, it may have helped the process get going faster. To do electrolysis you need DC electricity. At first, the only real source was primary-cell batteries, which are at least as expensive as the materials they're made out of, but Micheal Faraday built the first homopolar generator in 1831 and practical industrial-scale dynamos appeared (simultaneously from multiple inventors) right around the time in question.