Unless that "as" becomes a "before", we'll end up with both taxes.
We are in far, far more danger now of having both taxes than we will be after passage of HR 25.
Today, we enjoy zero protection against having both taxes. Hell they're already after internet sales. All it would take is a single vote in Congress to impose a sales tax on top of our income/payroll tax nightmare.
However, the nrst imposes a number of formidable obstacles. For instance, the entire income tax code is erased. How long would it take to rewite and renegotiate another income tax code? With all the lobbying it would be years. Second, all existing income tax records are destroyed, save those delinquent at changeover. It would be a difficult task to make folks return all of their personal info to the feds - businesses too. Third, withholding would have ended. How duumb would it be to for a pol to propose or vote for reinstituting withholding after we've had a taste of having our own money first?
So yes, it would be possible - but it is much more likely to happen now under our income/payroll tax sheme. The nrst reduces that possibility by eliminating the income tax code, destroying income tax records, and abolishing withholding of taxes. If avoiding having both taxes is your concern, then it seems you would be for the nrst. Go to thomas.loc.gov and search HR 25.