I tried it. It says somethin like this:
oops dont get fingerprints on it!
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[20:18] ryannissan: I get what you're saying. And sure, just as long as it's not two hours, SON
[20:23] Broderick1995: two hours my ass
[20:24] ryannissan: LMAO
Nothing really happens. It just says "! You got fingerprints on it..." I tested it, I guess it was some sort of abandoned plot... or some event that hasn't been released yet. :\
The guard leaves? I always get annoyed by that guard. I wish I controlled the character. That way I could get finger prints all over it. Or mabey throw my Torterra out of its pokeball and bam! Smash it
Yes I think it is between 4 and 6am according to my Nintendo guide the Guard is not there and you can touch the statue, it says you left finger prints on it.