Can an unplugged moldy refrigerator cause mold to spread throughout the house?
Mold spores spread on air currents and land anywhere in a house. However, the spots where mold spores may land must be conducive for the spores to survive and thrive, i.e., damp and preferably dark. There may be other areas of your house that are damp, etc., that produce mold, independent of the moldy fridge.
Is the door to it open? Spores are carried by the air, so it could if it landed on a surface that would support it. I would mask and glove up and clean it out with bleach solution and leave the door open so it stays mold free until used or removed.
Mold can grow almost any place where moisture lingers for very long. Many people have mold on their window sills just from condensation and poorly sealed windows. Mold will spread as long as you have moisture that lingers anywhere in your kitchen/house.
Some manufacturers forbid using bleach, ammonia and detergent to clean the interior compartment of the fridge. In addition, a major white vinegar maker instructs refrigerator owners to follow the cleaning instructions of the appliance manufacturer, and it does not necessarily condone the use of vinegar for the killing of mold.
I would strongly suggest that you make a very thorough inspection of the complete house to determine if you have anymore vulnerable spots so you can find the cause and fix it because mold is dangerous to your health. Be sure to check behind furniture, behind appliances, under the sinks, bathrooms, and especially closets.
Here is a site that gives good instructions on cleaning a refrigerator:
This is a good site for instructions on finding/removing mold in your house:
I don't think it could spread throughout the home, but it could spread onto adjacent counters. However, if there is mold in the walls or floors, and that is how the refrigerator got moldy, there is a better chance mold can spread throughout the house.