If the floor is in good shape, I don't see why not. But sometimes chickens will lay eggs under there, and you'll have a devil of a time getting them. My coop is off the ground, but the chickens don't have access under there. Maybe a photo of the coop-to-be will help us.
To move it - Brace it well with 2x4s from one side to the other in a x in the front and other end and on side walls a x with 2x4s. I suggest you set it on 4x4 treated post so the 2x4 floor frame is not setting on the ground - it will rot out. Here's a picture of what you have to do when it rots out. This shed is about 40 years old. The 4x4s that were under the wood floor rotted out. We cut out all the bad wood and transformed it into this coop below. The area under coop is part of run and now has hardware cloth on legs. The chickens have protection from snow and rain and shade on hot days. We have 3 coops that are all raised 2' off the ground.