2001 Honda Civic Ex 2 door overheating problem?

I have a 2001 Honda Civic Ex 2 door. I start driving down the road and it starts to overheat. I don't have a blown head gasket. I have replaced the water pump and thermostat. I would look under the hood and it looked like I was leaking. But my radiator was full and radiator overflow will bubble out then drain once car is cooled down. I found out my radiator fan aint working. Will be replacing that soon. But my question is, if the fan ain't working will that cause leaking some how? Question sounds dumb but can't figure out where it is coming from

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