Yes, it is possible for a Floyd Rose style tremolo system to go out of tune even though it is locked at the top nut and not used.
As touch on previously here, changes in temperature, humidity and other environmental changes, will cause the wood in the neck and body of a guitar to expand and contract. This will cause the tension on the strings to change, which of course leads to the pitch changing. This tends to be minimal if your guitar is kept in a semi stable environment that doesn’t change much. But, if you pull a guitar out of a cold trailer and walk into a warm bar to play a gig, you may find your guitar out of tune, or worse, some body checking might occur, small cracks in the finish. Hard tail bridge guitars and not immune to this either. Leave the guitar closed up in the case for a while to acclimate slowly.
However, the most likely reason for this type of trem system to go out of tune when not played would be the quality of parts and guitar. The original Floyd Rose double locking tremolo bridge was well crafted and designed with quality components. In many cases, the more commonly found “licensed Floyd Rose” trem system is poorly made and constructed with parts that are softer than the original design. The force of all the strings and springs is focused on two knife edge fulcrums which are set against two posts that are installed into the body of the guitar. If that knife edge, or the post, is not made of quality alloys, it will be reshaped by that force. If the wood of the guitar is of a softer quality “hard wood” the posts will shift and the screws that hold tension against the springs can move as well.
In short, the quality of the guitar and the quality of its components contribute to how well they play and remain in tune. As the old adage goes, you get what you pay for…. most of the time. If you make your living playing guitar, you don’t want to skimp on the tools of your trade. On the other hand, if you are an amateur or even an enthusiast and an out of tune guitar won’t destroy your career, then you can learn to deal with it. in fact, if you do get a FR style bridge you should learn how to change your strings and adjust the tension on it when you change your string gauge. In the end, when you break a string on stage in the middle of a song, you’ll want to have another guitar close by. Or, block your FR tremolo.