The wild card is the inspector between step 3 and 4. If you can get the inspection timed right you might be able to hold that schedule. Typically you lose a half a day waiting for the inspector before you can cover it up. They have been doing these around here (SW Fla) in a day and a half. Dig and set the equipment one day, get inspected first thing the next morning and backfill as soon as the inspector leaves.
You also have to add the price of resodding the yard and connecting to the house. Sod is going for $85 a pallet but the HO can do it. Just remember "green side up".