I have constructed a (huge?) house above ground(completely) in Terraria.
My NPCs though, haven't arrived. All the rooms are meeting the requirements mentioned on this page of wikia.
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Yes, as long as your rooms are considered habitable, NPCs will be able to move into them; no need to worry about your house being off the ground. :) If you're not sure about whether your rooms are considered suitable, open the menu and click the "house" icon above your equipment list, then use the "?" cursor on each room.
If the rooms are suitable, you can also try to assign the NPCs to your desired rooms by placing their icons on each room manually.