I haven't done this exact experiment, but honestly, I'd be shocked if you could hear ANY difference between a guitar with brand new strings, and one that had effectively brand new strings (only 5 min playtime) that has been sitting cased and unused for a few months. We assume, of course that the cased guitar isn't in some crazy high salt/high humidity environment, and that you tuned it to standard pitch and left it there, etc.
I can tell you from experience having done the second part of this experiment (put a newly stringed guitar in case then not played it for several months) that the strings still sound and feel new. . .and they're not automatically "broken in".
Its a different question, but I've also put 10 year old. . .but brand new in package. . . strings of different makes (Pro Arte, Augustine, plus acoustic steel and electric) strings on different guitars, and in every case the strings sounded like new and performed with no issues I could tell. All of these were in sealed plastic bags, stored in cool dry conditions.