Those self-stick tiles are apt to come up. If the surface underneath is not properly prepared, or the wood gets lingering dampness, they can come up real soon. I would not personally bother with them.
If you have some scrap vinyl flooring (like, for free - I am not suggesting you buy it) you can staplegun it down and it will be a reasonable solution. It is FINE that you've already put the walls on, it is actually better to put vinyl down AFTER the walls are up rather than to run it under their sills.
Honestly though the thing that makes the most sense is to get some cheap-or-free paint remnants and paint the floor. If you can do deck sealer you can do paint; and paint is arguably better and certainly easier to come by "cheap or free". Several thin coats, on a tack-cloth-wiped surface.
How long totally naked untreated uncovered plywood lasts would depend on how much moisture is there. But it is easy to have waterer spills, rain blowing in, mud tracked in, etc... also they WILL scratch some of the floor bare at times (esp. if you are trying to chintz on bedding) and poo will cement itself down much worse to bare wood than to painted.
How much bedding to start with is a matter of personal taste, but I would suggest something in the realm of 2-4" at least, more if you have bare unpainted plywood.
Good luck, have fun,
Pat