Thinking it over, a better question would be whether at storage temps of 32 - 40F would unripe peaches sustain injury that would prevent further ripening when put back at room temperature.

Peaches need the sun to obtain full sweetness, so I presume that once you pick them and refrigerate them, that the sweetening process would stop. They will still soften up, but that's it.

creekweb:

What I've read several times is that some stone fruit cultivars are damaged when refrigerated others aren't. Breeding cultivars that don't suffer damage is a stated objective of some breeding programs so it's a real issue.

The injury when it occurs is at temperatures above 34F. 32-34F is the best temperature.

I've not had injury holding my fruit for up to 2-3 weeks and I think I'm above 34F.

The classic damage I've seen is fruit from Chile that is shipped up on a boat and suffers internal breakdown.

I'd say you need to try it and see what happens.