Funny you should ask this Russ. As a teen, when I got what I consider my first real instrument -- an Ibanez ST300 electric -- I also got for my b-day, a new digital clock -- oooh! This was in the days when alarm clocks were mostly the kind with the little flip cards
My new digital clock had the standard 12:00 little soft plastic thing on it, just like what you're talking about. For some reason, I put it on the back headstock of my guitar. There it stayed for many years. In college, a bass player friend/roommate saw it and asked me about it. I told him how I'd had it there for years, and he thought it was funny. When he ended up getting a new digital clock, it came with the requisite 12:00 plastic thing, and he also put it on the back of his headstock.
This started a little private joke amongst our musician friends, who also started doing the same thing. The Ibanez is long gone, as well as at least four other guitars which also had them on the back. I once even saw a guitar on craigslist somewhere in which someone also had one on the back of the headstock, and it made me LOL. :lol: The last one I had one on was my '76 Strat. I actually think I still have the original clock label in a bag with guitar tools somewhere.
To answer your question. . . they never did anything to the finishes -- both polyurethane and nitrocellulose. Granted, I always store all my guitars in their cases except for the favorite I'm currently playing, which usually is on a stand. I never leave them in sunlight either. I think that if I did, the heat and UV light may react with the plastic, causing off-gassing. Therefore I wouldn't be surprised to see a little rectangle, possibly with a 12:00 as well on the back if I did.
The moral of the story is, if your guitar usually lives out of the case, I wouldn't take the chance. If you keep it in the case most of the time, from my experience, it won't affect it.