Can I shut off a second water heater?
From your picture it appears they are paralleled. 

To be seriesed the cold water would enter only one of them and the hot output from that one would be fed into the other's cold water input.

That is not what you have here. The cold water feeds both of them and the hot outputs are tied together. That makes them paralleled.

If you shut the gas off to one of them, the water to that one needs to be shut off or cold water will flow through the heater directly into the hot lines. You will need individual water shut offs installed on the one that is shut off. ThreePhaseEel is right, there should be individual isolation shut offs on each pipe of each heater.

Happy Turkey Week!