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Hmmmm, batteries were not unknown during the middle 1800's. They were primitive by today's standards, naturally. But it may surprise you to know that the concept goes all the way back to the ancient Persians, who actually had crude, but working, models.
A form of electroplating was known to have been practiced by them.
And the Leiden(Leyden) jar was in use 100 years before the American War of Secession. It is also a fact that the first electrical doorbell was invented by Joseph Henry in 1831. Granted, such things weren't in wide usage but their properties were known. One might even consider them "cutting edge" for the time.
so, it is remotely possible that some clever civilian engineer, once in the Army as an officer, brought the idea to his battle front lodgings. It's a stretch, admittedly. But stranger things have happened.
As for re-enactors, well... they are all about authenticity. I wouldn't include the electric doorbell in a re-enactment camp unless I could document it's usage from the period.