Addressing the original question, heat will always flow from hot to cold and insulation does not stop that flow but only slows it down. Using a "noodle" to insulate a pipe slows heat loss in all directions will only keep pipes from freezing if the water in the pipe can be replaced with warmer water from time to time. Continuous insulation over the top of the pipes in the attic will slow heat loss to the outside, and if the inside of the house is still above freezing, the pipes shouldn't freeze with the second scenario. If you don't have insulation over water pipes in the attic, then the heat in the attic in the summer can heat that water in the pipes to over 130 degF.
On a second topic, a portable propane (or kerosene) heater used to heat inside a home will put products of combustion into the home, which include Carbon Monoxide, Carbon Dioxide and water vapor.