Since you don't have an accumulator tank, you should not really have water running without the pump (assuming you aren't connected to city water). There might be a really quick spurt from the pressure in the piping, which is slightly elastic, and the small air space in the water heater, but not a more continual flow. If you're hooked up to city water, there's generally no reason to have the water pump on at all.
Anyhow, the only way you generally can get hot water in the cold lines is if the bypass valve is not set properly (i.e. open) or there's a shower with the hand knobs on and the valve at the spray head shut off, which amounts to the same thing. While more commonly it's the outside shower that gets overlooked and not shut off fully (because of how it's often used to rinse stuff off and because it's more out of sight), the inside ones will also behave exactly the same way.