Can I install sheet vinyl over ceramic tile without adhesive?
I have seen vinyl floors where the glue was put down unevenly (sparingly in some areas), and by comparison the areas without enough glue were visibly damaged on top from wear. So, I think that (for whatever reason) vinyl floors which are not (well) attached have a shorter lifespan.

However, you might want to look into floating vinyl floors (here's a random link for a floating vinyl floor vendor). Perhaps it would help to lay some carpet padding on the underside, so that it doesn't slide and protects the original floor. 



Now, I have often seen vinyl floors that are made to look like tile, stone, or wood, but they are always reaching for a conservative aesthetic. If you already have a sheet of vinyl that you like, then you are sort of forced to install it properly or be willing to sacrifice it to a learning experience.

But I have always wondered if you could create vinyl panels from say, 3/4" plywood. Basically the idea would be to cover the top with the vinyl and the bottom with say, foam rubber or carpet padding, and then just lay the panels down and cover the seams with trim. Unfortunately, I've never had enough money to warrant an experimental floor, so I can't really recommend it; but if you try it, let us know how well it works, any tips or hiccups, and after a while- how long it lasts.