Does the part of the air conditioning system that sits behind the house with the fan on top need any type of regular cleaning in the spring?

You will want to make sure the fan area is free of any debris, such as leaves and branches. Also, you will want to make sure that the fins are clear of dirt and debris on all sides of the unit. Use a gentle spray of water from your hose to clean these fins. Do not use high pressure as that can bend and damage the fins.