In The Lost Hero, when Piper wakes up from being a gold statue:
Piper woke up cold and shivering.
She’d had the worst dream about an old guy with donkey ears chasing her around and shouting, You’re it!
-The Lost Hero, chapter 33
She obviously wasn't aware of being gold, i.e. she couldn't look out her own eyes and she wasn't a disembodied consciousness.
However, looking at other golden statues like Midas's barber, they (presumably) look the same as they did a long time ago (or else somebody would have noticed that they're a pile of dust).
Piper wasn't aware of time passing, but she dreamt, so she had some brain activity thus time was passing for her. But what about the other people? Does time just move really slow?