No he isn't.
If ( just for the sake of the argument ) RMB replaces USD as the international currency base, US has absolutely nothing to back dollar value and prevent it from dropping.
Which, it turns out, works just fine -- the belief that gold has value is roughly as magical as the belief that saying some words can turn wine into blood (and a prime sign of religious dogma in both cases).
The US economy may be fucked up in many ways, and may face some harsh transitions if it can no longer rely on the strength of the dollar as an international currency, but it is still a large economy. The loss of that strength will not magically result in the dollar having "no backing".
Certainly, if the dollar was replaced by the RMB internationally, the dollar would start to drop against other currencies - until it reached a realistic equilibrium point.