No by just making it illegal to buy sell or trade with along with rewards to turn people in.
That’s worked so well with drugs and years ago, with alcohol.
Seriously,Gresham’s law says good money drives out bad. People, despite laws and regulations will always prefer gold and silver to paper.
Also, once the paper is completely worthless what are they going to pay the rewards with?
The Chinese and others with goods to sell will be willing to take precious metals long past when they are willing to take FRNs. The only issue, like you say, is that the government will make it illegal. All that means from a marketplace view is that there will be third parties who will take the risk of trading in PMs and you won't get nearly as much for your metals as when they were legal. But that deal will still be orders of magnitude better than the FRN deal.