What would cause a sudden drop in humidity in my home?
the humidity is caused mainly from sources of water in your home such as plants, pets and of course humans. As you breath out water is coming out of you. And the condensation of water on windows is caused by different temperature outside/inside especially at the interface glass/air.
There is no way that heater can reduce humidity in sealed room (in means of decomposition of water as you suggested). Imho if you have CO alarm you have nothing to be afraid of.