True, if the engine coolant temperature sensor tells the computer that the engine is too cold and fuel enrichment is needed.
Your dash gauge may or may not be telling the truth. Yet the cold enrichment commanded by your computer is very brief. It is not likely that you have a problem other than your gauge is not where you think it should be (which may not be a problem at all).
As for fuel economy, which is a pretty good diagnostic tool, it must be done precisely in order to have valid results. Do this by keeping a notepad in your car. Fill your fuel tank fully every time you gas up and record the mileage. Divide the number of miles travelled by the number of gallons needed to refill the tank. That is the only way to truly track your MPG accurately. It helps to note which weeks you do a lot of long distance driving and which are in stop-and-go traffic.