It depends on how the fan control circuit is wired. If you have a Fan On/Auto switch, yes it will blow cold air if the switch is put to On.
Yes
The water continues to run into and out of the water heater. There is just no flame to heat it up.
Pilot light alone will not produce enough heat to damage the tank, but the main burner will destroy the tank and possibly start a fire. Why would anyone want to leave the pilot light on an empty tank?
Turn knob to PILOT, press button down and light the pilot; hold button down for 60 seconds and release - pilot should remain lit; turn knob to ON. If pilot does not remain lit, turn knob to OFF, wait 5 minutes and try again, If pilot still will not remain lit, replace the thermocoupler.
The pilot setting will heat the water a few degrees. A gas water heater will have a thermal rating in BTU of 30,000 to 80,000. The pilot light by itself will have about 1,000 BTU. Operating overnight with no water movement and a well-insulated tank, you will observe a temperature rise but certainly not enough for clothes washing, dishwashers, or showers.
The thermocouple is usually the first thing to change. It controls the valve and the spark ignition is just to light the pilot.
If it is windy outside, you may be getting just enough of a breeze to blow out the pilot light -even though the covers are shut. My heater is in the garage, and even w/ the garage door shut and the covers on the heater shut, very windy weather can still cause enough of a draft to blow out the pilot. You could try to find something to block drafts around the heater such as a hot water heater blanket.
Sounds like you need a thermocouple.
A number of problems can cause a swimming pool heater not to work. The most common I have found is lack of water flow. A heater needs a certain amount of water flowing through it to work correctly. The next most common problem is due to the pilot not lighting or remaining lit. This is usually due to the pilot generator not working. When you light a pilot light and have to hold it for a length of time before releasing the button you are allowing the pilot generator to heat up and then stay open to keep the pilot lit. Usually you need a licensed person to do work with changing items on a gas unit. The thermostat can be a problem for any water heater. Most of the heaters I have worked on were gas. If you have an electric heater waterflow still needs to be checked and the electrical connections can become corroded in the presence of chemically treated pool water.
To troubleshoot and fix a Honeywell pilot light that is not staying lit, first ensure the pilot light is clean and free of debris. Check the gas supply to ensure it is reaching the pilot light. If the pilot light still won't stay lit, the thermocouple may be faulty and need to be replaced.
Still trying to find out who the pilot was... The co pilot was Navy officer Robert V.R Ware.
Pilot light would work but the main burner would not as the thermocouple proves that there is a pilot light to fire. The main gas valve would not open