No, the $100,000 house would cost $100,000, with 23% of the taxable amount(*) of that $100,000 being remitted as taxes. the NRST is a repalcement tax, not an additional one.
(*) The taxable amount on a new house would be the amount over the valuation of the unimproved property -- the property itself is "used" by definition. A resale house would have no sales tax since it is considered previously taxed.
There are implications to what you are claiming here. First, you assume that there would be no corresponding increase in the money supply. Because you assume that, you must also recognize that everyone's income would decrease by 23%.
You see, currently, our incomes are pre-tax. Under the so-called "Fair Tax", our incomes would be post tax. I currently pay my son's daycare $100 per week. That is the day care's total income (and the director pays tax on that). With your assumptions, under the falsely named "Fair Tax", her income would be $77 per week because she would have to remit $23 to the government.
(If there is a corresponing increase in the money supply as the government predicts, prices of everything would go up by the amount of the tax. I would now pay $130 per week for daycare, the director pays the government $30 and retains the same $100.)
This relationship holds true regardless of what industry you are in.