Re: large hole in vinyl flooring
There's only one way to know if the peel and stick tiles will be thicker or not and that is to cut out a piece of the existing vinyl and match the thickness against the tile. Another route would be not to worry about it at all. While a ridge isn't exactly aesthetic, neither will an island of P&S tiles in the middle of the room. No patch is going to look good, but you can change what you're doing from a blatant patch to more of a "designer" look. How about installing a patch of Pergo under the desk area? It should hold up to the chair pretty well, and it can be trimmed out on all sides with a reducer to transition it back to the vinyl floor. This would look much better than P&S tiles and you wouldn't have to tear out the vinyl to do it.
If using a Pergo or Pergo-like product, don't bother with the vapor barrier or padding under the material, it isn't necessary in this instance.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!