There is no evidence to suggest that dollars will be backed by BTC officially.
And to be honest there is also no signs of pointing towards this.
Us dollars have a lot banking on them first of all usd is the global world reserve which means that their decisions over their currency can have worldwide effects that need to be considered carefully. A global reserve would not want a currency that is unstable and frequently fluctuates like bitcoin.
To us, bitcoin’s limited supply is a good thing but as a reserve this is another reason for bitcoin to be a questionable asset for the government.