Are squirrels nature's little speed bumps?
What would be the point? You'd be putting hot water into a water heater which would then do pretty much nothing until it cooled back down. The electric heater isn't going to turn on until the water in there has cooled down enough to trip the thermostat. If you're running out of hot water then you need a bigger heater with more capacity, not adding another heater into the same system. If you run all of the hot water out then you'll just be using the vent free heater since the electric wouldn't have time to heat up water as it runs through the tank.
Are the fire alarms for detecting fire only or CO as well? Are there connected to power (with backup batteries) or just batteries? If all the alarms and the radios are connected to the same power line, perhaps that line is experiencing some problems - like oscillating voltage that triggers the alarms.