I live in 1/2 of a house with a basement-located gas forced air furnace. I have a large floor register in my kitchen that is about 40% covered by a refrigerator and a shelving unit. Other than reducing the amount of heat coming out of the register, will this harm anything?

 

Welcome to the forums

Typically covering one is not an issue but how many others do you have?

 

Most furnaces except the newest produce a fixed amount of heat, and depend upon a high air flow past the heat exchanger to strip the heat produced from the furnace and prevent it from over heating. If the furnace over heats, a limit switch shuts off the burner until the furnace cools off.

Overheating the furnace like that can cause cracks in the heat exchanger, which can be a safety hazard that will required replacement of the furnace.

Also, while the situation described above allows the furnace to heat the house during moderate weather, when the weather gets especially cold the burners wont stay on long enough to keep the house warm.

During the coldest weather, the house will never warm up.

Is your floor register a warm air vent or a return air vent, sucking cool in for the furnace to heat?

Is this a forced air system with a fan forcing the air around? Gravity warm air systems with no fan usually have "large" grates.