tl;dr, no, gold and precious metals aren’t going to hold any significant value, there’s essentially zero demand and very high supply.
The thing you’re missing with respect to precious metals is they have never been pure currency, they’ve always been rare and durable trade goods with high intrinsic value due to workability and ornamentation. Their use as a currency is built on top of this durable value, it’s not independent of it.
The problem is, for that intrinsic value to be realized, you need societal stability. In other words, there need to be enough people wealthy enough to value the precious values as ornamentation, if not enough of these people exist, they have no value. For most of human history, society has been “stable enough” for this to hold, which is why it seems obvious to treat this as a universal truth. In the cataclysm though, what demand is present is trivially realized by looting homes or jewelry stores, leading to essentially zero unsatisfied demand.
To some extent even in the absence of immediate demand, you could anticipate future demand and assign value based on that, but again in the dda scenario, there’s a supply glut as well as bottomed out demand, and even worse, no expectation of that demand increasing in the immediate or even medium term future. There is potential that some people would be in denial about the scenario, but that isn’t going to be enough to drive overall demand meaningfully.