I'm unaware of any FairTax systems being implemented in an actual real life situation, but there's a (length) article on the subject detailing about a simulation: Jokisch, S., & Kotlikoff, L. J. (2005). Simulating the dynamic macroeconomic and microeconomic effects of the FairTax.
The article is very positive about the potential implementation of a FairTax system. To be fair, the article was written in 2005 - well before the economic decline - but the simulations are done on a long term basis, so they should still be considered viable.
According to our simulation model, these policy changes would almost
double the U.S. capital stock by the end of the century and raise
long-run real wages by 19 percent compared to the base case
alternative. They would also preclude a doubling of the highly
regressive payroll tax. Indeed, the poorest members of each cohort
experience remarkably large welfare gains from the FairTax. To be
specific, today's elderly poor are predicted to experience a 13 to 14
percent welfare gain. In contrast, their middle class counterparts
enjoy a 1 to 2 percent gain, and their richest counterparts experience
a .5 to 1 percent welfare loss. Poor baby boomers experience 8 percent
gains, while middle- and upper-income boomers experience either very
small welfare losses or small gains.
Yes, some initial high- and middle-income households are made worse
off, but their welfare losses are minor compared with the gains
available to future generations, particularly the poorest members of
future generations. The economic and welfare gains from switching to
the FairTax are somewhat smaller if one models the U.S. economy as
fully open to international capital flows. But these gains are
nonetheless large and very significant.
The general consensus of the article seems to be that while the current US tax system benefits the aging, it is damaging to the macro-economy on a broader scale. The base case simulation (as executed by Jokisch & Kotlikoff) underlines this. The model predicts a major reduction in take-home-pay for average workers. FairTax is presented as a cure - not only does it increase general nett salary, it also has a levelling effect on the economy as a whole, benefiting the less well-off. While there is an ever so strong opposition to levelling policies in the US, on a global scale (e.g. in Western Europe) it's a more accepted approach.