The fake Construction Yard serves to deceive enemies into targeting them to draw attention away from the real ones. It can also be put into outpost bases to make them appear as full bases, though the fake Construction Yard itself is unable to provide ground control.
To make it more convincing, the fake Construction Yard can also be unpacked into a fake MCV.
In Exist to Exit, both Construction Yards at the top left and bottom right Epsilon bases are fake, the only true one is the dark purple Construction Yard where Epsilon will deploye at the top right shortly after the beginning of the mission.
In Meltdown, even the only Construction Yard on the map is fake.
In Gridlock and Earthrise, there is an Epsilon Construction Yard located next to the player base, which is obviously fake.