Does deleting a save file remove any houses saved to gallery?

The Gallery is an online repository of builds and households so it will remain until you remove it manually regardless of save data.

The "Library" is a personal repository of households/lots that are saved to your computer; however in a different file than your "core" save data. This means if you delete the saves in-game your library will still be there in the next new game or w/e; However, if you do a full wipe of your hard-drive and/or somehow otherwise remove the separate data files for the library they will be deleted too. Also the directory your library/saves are in is directly tied to your Windows User Account, even when using the same origin account (this is because they are stored in the My Documents Folder). So if you login to a different windows user then you will temporarily "lose" your library and saves from the original account - as they are saved in a different location on your PC; Your "Gallery" However (or shared Lots/households) will still be available to you by accessing your Gallery Tab and clicking "View Catalog" where they can be (again) downloaded into your current save file directory.

Edit: I just noticed you said "Xbox one" - which I have no experience with; however being a Microsoft product I would /highly/ doubt the conditions between Windows and XBOX are very different.